Whether or not higher scores predict anything (other than how people are likely to do on future exams) is unclear.
The performance distribution on all tests like this is very steep around the mean. Small changes in absolute performance will herald large changes in percentiles. The same is true for the MCAT also. The difference with the MCAT is that people with scores at the mean or below often don't get into med school at all. So when you look at all the higher scorers, the absolute differences tend to be a bit bigger. MCAT doesn't release absolute percentages as far as I know but I expect you'd find the same thing.
Regarding psychometrics as described by
@Med Ed, although in general that's true and often argued by the USMLE as a reason not to use scores, it's also not really applicable because the USMLE isn't a test designed to assess minimum knowledge. If you really want a minimum knowledge test, you create it such that most people will get 100% of the questions correct. A written driver's ed test is a good example of this. It's designed so that if you know the basic material, you get everything correct. And by inference, the passing cut off tends to be relatively high. Another example are the innumerable online HR modules I need to complete each year -- each has a test, I need to score 90% to pass, and getting 100% is usually very easy. (Pointless aside, I am really annoyed when these tests have a minimum pass of 90% but only have 5 questions)
That's not the USMLE exam design. The USMLE is designed as a general knowledge test with the mean in the middle. The minimum pass level is theoretically picked to define minimum necessary knowledge. But the score clearly represents the taker's knowledge as measured on a MCQ test.
Not to nit pick, but the standard deviation doesn't tell you whether a score of 250 is different from 260. That's approximated by the standard error of measurement, which is much smaller (about 9 I think). And even that doesn't say that scores within 9 points are "indistinguishable" -- unless you want to make that statement with 66+% certainty.