There are problems with that story
To start with a technicality, Alaska and Hawaii did not become states until 1959, so all-states-but-one would have been 47 states in 1955.
Yellow lines were already supposed to be used in certain circumstances in 1961. In 1961 edition of the Manual on Uniform Traffic Control Devices, part two:
2B-2 Center Lines on Rural Roads
The center line on a two-lane paved rural highway shall be a
broken white line, [...]
On four-lane undivided rural pavements, or on pavements of a
greater even number of lanes, the center line shall consist of two
solid yellow lines [...]
2B-3 Center Lines on Urban Streets
The center line on a two-way city street with less than four lanes
for moving traffic at any time shall be a solid white line. [...]
The center line on a two-way street with four or more lanes for
moving traffic at all times shall be a double solid yellow line
except on a street involving reversible lane control.
2B-8 No-Passing Zone Markings
A no-passing zone shall be marked by a solid barrier line placed
as the right-hand element of a combination line along the center
or lane line. This barrier line shall be yellow.
As these quotes show, there were times when yellow lines were to be used and times when white lines were to be used.
One thing that the story does get right is the change in 1971. The 1971 manual's part three has the following:
3A-5 General Principles-Longitudinal Pavement Markings
Longitudinal pavement markings shall conform to the following
basic concepts:
- Yellow lines delineate the separation of traffic flows in opposing
directions or mark the left boundary of the travel path at locations
of particular hazard.
- White lines delineate the separation of traffic flows in the same
direction.
So here we see that yellow lines did indeed become the standard divider between opposing directions at that time.
There has been at least one study about switching to all white lane lines. Among the reasons for possibly switching they list
- All other factors being equal, white markings have higher retroreflectivity than
yellow markings.
- Most of the industrialized countries of the world use all-white pavement markings.
The study advises against switching because of the cost of implementing a switch and because drivers are already used to yellow lines. For safety, they say
Safety is a factor in any potential improvement to the transportation system. At this time, it is not possible to assess the possible reductions (or increases) in crashes that would be associated with implementing an all-white pavement marking system.
Looking at a chart of fatalities, there's no obvious change in the early 70's when yellow dividing lines became the standard. Do note that this is only fatalities, which would not show any effects on accidents in which fatalities were unlikely to occur.