Answer: Seemingly yes.
Bonus: Probably simpler than most people think.
First off, this is a great question. I've heard many people claim this is true, though not having a remote keyless system, haven't had a chance to do it myself. Looking it up online, there's virtually no "official" information about why this works. I'm going to list the most credible sounding reasons/sources I could find, explain why I think they're partially right, and then propose a mechanism.
There's a New York Times tech article that has a small section on remote keyless systems. Quote:
The trick turns your head into an antenna, says Tim Pozar, a Silicon Valley radio engineer.
Mr. Pozar explains, “You are capacitively coupling the fob to your head. With all the fluids in your head it ends up being a nice conductor. Not a great one, but it works.”
(The article also talks about freezing hard drives to bring them back to life, a somewhat contentious issue that's been addressed here as well: Freezing your hard drive to recover data?)
There's also an article from Tom's Guide that mentions capacitive coupling. Quote from the 4th page:
I recently had the chance to meet several engineers at Intel, including radio expert Robert Paxman. He told me: “It comes down to antenna efficiency. If a transmitter operating at ‘x’ frequency range has an antenna that might be lacking in efficiency and you couple it to something that creates a situation for better efficiency, getting that added range is plausible. Because the body has some conductivity, placing it close to some body part would create a coupling effect. Think back to the days of TVs having “rabbit ears” for antennas. Sometimes the best reception and clearest picture was had when you were touching it. The same principle applies here.”
Finally--and we're getting into un-credible territory here--a post about LC circuits on Physics Forums got me thinking. Quote:
One of the main components of any radio tuner is called the "LC Tank" or "LC circuit". http://en.wikipedia.org/wiki/LC_circuit It's a very simple circuit and the frequency it resonates to (is tuned to) is given by:
f = 1/(2*pi(sqrt(LC)))
You can't really have much effect on "L" the unless you come into direct contact with the circuit. "C" however is the capacitance and will be affected by conductive bodies close to it. Proximity relationship is exponential... that is 1" away is far more of an effect that twice the effect from 2" away. So as your body comes into contact with the plastic body of the fob the value of C has now changed.
Everything these three sources put forward is mostly correct. Your body does indeed act as an extended antenna, and that's why contact and body position can help clarify the signal on a radio or TV (or any) antenna. But that's receiving. When transmitting, there are a few items of importance: antenna shape, antenna orientation, and transmission power. Transmitting a more powerful signal would be the easiest way to overcome all of these issues - a bigger battery for the key fob would mean a stronger, longer signal, and that's all.
But that's usually not a simple option, so we work at optimizing the orientation. What most people talking about this issue seem to forget is, as long as you're holding the fob, you're part of the antenna. Touching it to your head is just changing the overall orientation, not suddenly turning you into a magic instrument - you're always an antenna. Does putting your head against a set of rabbit ears work better than adjusting with your hand?
As a slight aside, the whole changing capacitance idea makes no real sense. One only has to look at the equation posted above to see why (ironic that it was posted as a reason that it does make sense). Frequency is inversely proportional to capacitance (since C is in the denominator of that equation, a larger capacitance = larger denominator = smaller frequency), so as capacitance increases, frequency decreases. If the transmitted frequency changes too much, the receiver just won't receive any signal, since it's no longer looking for the "right" broadcast. Designers had to have had this in mind, so it's really doubtful that by touching the fob or the key you're really changing much at all about the inherent transmission properties. Again, what matters is orientation... one part of the body over another shouldn't really make a difference (re: the first quote, if liquid is the mechanism, your head definitely doesn't have more liquid in it than, say, your torso).
I'm betting what's likely here is a kind of pseudo-confirmation bias. You're expecting it to work when you hold it to your chin or temple or wherever, and you see that it does, so that's it. But it's pretty clear that people are doing this outside on the street or in parking lots where many variables are unaccounted for rather than in any kind of controlled environment. If it stops working at hip level but then works against the chin, that's all well and good, but you've only done the test in one of 360 directions. Ten feet over it might work just as well in the original orientation.
I think the best explanation is that it's a combination of height and directionality. The higher you hold the fob, the longer the transmission can go. The receiver's location on various car models is bound to differ, but by holding the transmitter higher up, there's far less chance of obstructions interfering with the signal. Same reason radio towers are tall or on top of tall buildings/land formations. And by holding the fob against your head, you're unwittingly creating a transmitting loop antenna with your arm and body (far larger than the tiny circuit loop antenna inside the fob), so this is probably helping as well (holding on chin vs. temple will alter the directionality by 45°, further changing efficiency depending on where your car is).
Untested, but if you try holding your keys a la He-Man and saying "I HAVE THE POWER," you might get the best results yet.