I paid close attention to the Fukushima investigation for years. I've lost my sources (I could use some help with that) but I can add some more detail as to exactly where it went wrong. If the lack of refs is a problem, I'll cheerfully delete this answer.
Yes, as you say, the earthquake didn't do any critical damage inside the containment area, but the tsunami took out the diesel generators and switchgear. That left backup methods of cooling the reactors, and I'll be talking about unit 1 exclusively. Staff had a plan to save all the reactors, it was a good plan, and it was working. This plan focused on saving units 2-3, which were more time-urgent. Unit 1 had a "longer fuse" because it had a cooling system called an isolation condenser. It would run indefinitely if the tanks were kept full.
The isolation condenser
It is a steam-to-water heat exchanger at the top of the reactor building, well above the reactor. On one side is plain, clean water at atmospheric pressure, which boils at 212F (100C). On the other side is pressurized primary-loop (radioactive) steam at reactor pressure (so higher boiling point).
The system is passive and requires no power, just occasional refills of water.
The pressurized reactor steam boils the clean water in the IC, and this clean steam is vented to atmosphere. This condenses the reactor steam into liquid water (still pressurized at reactor pressure), and the water (via its own weight) drops back down into the reactor (the significant height provides a "head" of pressure on top of the fact that it's already at reactor pressure, effectively injecting it back into the reactor as makeup water). Since it's the same water, there is no water loss, water level does not fall and the core is not uncovered. Instead, the IC loses "clean" water, and this must be made up. But any fire truck can do that since it only has to lift water to the top of the building, not inject it against reactor pressure.
The IC is so effective that it is included in the newest reactor design, the ESBWR. In that design, the IC gets a 3-day supply of water. However, older Fukushima 1 only held an 8-hour supply. And staff knew that.
The IC rooms are high up on the reactor building, not in containment, and are in spaces accessible while the reactor is running -- though up many flights of stairs. The valves are there, and can be motor-driven or hand cranked. Their position can be observed. There are also water level gauges.
Good boiler stewardship
Staff had no idea they were heading into an INES 7 disaster. They expected their skill would save the reactors and they'd be back online after a year or two. So they practiced good "boiler stewardship" - which says you cool any boiler slowly, over time. Changing its temperature too quickly results in stress and the possibility of very expensive damage. The isolation condensers were cooling it too quickly, so they were cycling the isolation condensers on and off intermittently to achieve the target cooling rate*. They did this in the control room using switches to operate the motor-drives on the valves, and looking at indicator lights to see the positions of the valves.
When power failed, they kept doing that until battery power also failed. At this point, the motor controls and indicator lights went dead. They were not clear whether it was on or off. Now, to check it or change it, they'd have to do some stair-climbing. (But, fair chance, no one had ever done that).
The Pig's Snout
Instead, they decided to look outside of the building at the IC's two vent pipes. These are called the "Pig's Snout".
They saw steam wisping out of the "Pig's Snout", and concluded the IC's must be functioning.
They had never used the isolation condensers.
I recall reading commentary from reactor operators at a plant in New England, which does exercise their IC from time to time. They said when it's on, you don't get wisps. You get a solid blast of steam. It's unmistakable. But Fukushima staff didn't know this. **
That book also opins that the isolation condenser had never been used because while the operator was opening and closing one valve, three other valves had been closed. That opinion doesn't hold up. First, the IC initially came on automatically, which would have opened all four. Second, closing those valves would be a bizarre thing to do, given their intent to cycle the IC. Third, the theory conflicts with a field inspection of the isolation condensers (which shows considerable use of the IC water (one tank at 66%, the other at 83% @ 8:07), and 1 of 2 valves open per tank.
As a sidebar, the video raises an interesting point: this topic isn't widely discussed or reviewed, and very few people are looking at the hard data. I suspect that's because "the tsunami did it" is a neat, comfortable answer wrapped up in a bow, that satiates pro- and anti-nukers alike. I've been aware of the inspection video for seven years, yet it has only accumulated 750 views at this writing. It also follows that there is not a large body of written documentation on this subject; at least not enough for there to be much on the Web. This is typical of the media's disinterest in gory details: see also the Oroville accident and rebuild, and blancolirio's sole coverage of it. Many big events don't have a blancolirio, so the details (and refs) fade into obscurity.
The point of no return
With the IC offline, the reactor cooled a different way, which caused steady loss of coolant. Uncovery (exposure of the fuel rods) occurred. This broke the isolation condensers. Exposed fuel rods will overheat to where their zirconium shell reacts with steam to make hydrogen gas. It is very light. It went straight to the top of the reactor and the isolation condenser. Hydrogen gas does not condense, and it displaced the heavier steam, rendering it non-functional. Staff was not aware of this. They restored DC power, discovered the IC off and turned it back on, but it was ineffective. They did not realize this at the time, since a water-level gauge incorrectly indicated high water in the reactor.
After failure of the primary instruments, they did not look at secondary instruments, but instead relied on ad-hoc indication methods to determine if the isolation condenser was working. Because of inexperience with the system, they misread it. This unexpected early failure interrupted all the other recovery work.
* Fukushima Nuclear Accident Independent Investigation Commission report to the National Diet of Japan, p. 29:
5) The isolation condensers (A and B systems) of Unit 1 were automatically activated at 14:52, but the operators of Unit 1 manually stopped both IC systems only 11 minutes later. TEPCO has consistently maintained that the explanation for the manual suspension was that “it was judged that reactor coolant temperature change rate could not be kept within 55 °C/ hour (100 °F/ hour), which was the benchmark provided by the operational manual.”
** The 2011 Fukushima Nuclear Power Plant Accident: How and Why It Happened -
Tekijät Yotaro Hatamura, Seiji Abe, Masao Fuchigami, Naoto Kasahara, Kenji Iino, p. 37:
One of the reasons why the operator on duty did not recognize the fact was because no one had ever experienced the IC in operation. The best knowledge that anyone has was having heard from former operators that when IC was in operation, steam from the condenser cooling twater would blow out horizontally from the exhaust openings (the so-called pig snout) to produce lightning-like static and large thunder-like sounds (figures 2.15 and 2.16).