"But, if the RT is 500ms in A and 550ms in B, we know full well that the neurons in any one region were not firing for 500ms in A and 550ms in B. "

By putting in 500 ms and 550 ms, you are not hypothesizing that neurons are firing for 500 and 550 ms respectively. You are hypothesizing that BOLD activity is *linearly related* to these values.
I think this is an okay starting assumption. It would be interesting to what happens if you use some transform of RT, like log or a polynomial, and it is ceartainly possible that it may capture more or less activity. (For accounting for effects of frequency, people use log frequency and not the raw frequency, by the same logic.) For RT, I don't believe the best transformation to account for BOLD activity is well-known. Simple linear regression does seem to capture the "usual suspect" areas like frontal and pariatal regions. The only transformation we have used is to subtract the mean and divide by std. deviation, but as I said, other transformations may be interesting.