First, let us define "grade inflation" as "higher grades compared to other schools around the country." Sometimes, when people talk about grade inflation, they actually mean the gradual inflation of grades over time (where, over time, more and more A's are awarded and fewer and fewer C's, similar to inflation of a currency), but I'm pretty sure that's not what people mean when they look at the average GPAs of Harvard/Yale/etc. compared to the average GPAs of BU/BC/etc. So we'll use that first definition.
Now, say Selective U. is more selective in its undergraduate admissions than E-Z U., but because the average uGPA of students at Selective is much higher than the average uGPA of students at E-Z, you still suspect that there is grade inflation at Selective relative to E-Z. To discover whether this is the case, we need to compare the gap between the average high school GPA (a measure of selectivity, albeit an imperfect one) of each college's students to the average undergraduate GPA of each college's students. If the gap between average uGPA is greater than the gap between average high school GPA, you'd have a case for the hypothesis that there is grade inflation is Selective U. If the gap between average uGPA is actually smaller than the gap between average high school GPA, it seems there would be a case for arguing that there is grade inflation at E-Z U., not at Selective U.!
Well, this is exactly what we did when looking at Harvard College and Boston University.
Ok, yeah, I don't think this works. At the very least, it's building in a lot of assumptions that you're not acknowledging. A few problems:
* Harvard and BU aren't pulling from the same high schools, and there's no reason to think that the high school grade schools are comparable. One might argue, for instance, that Harvard is more likely to get students from the sorts of preppy high schools that offer grade bumps for AP/accelerated (which is the only way that they could be maintaining that 4.0 average, given that I'm sure Harvard College lets in students who got less than 4.0). Basically, if the grade inflation at Prep-High relative to grade inflation at Regular-High is more than the grade inflation at Harvard relative to BU, your method will conclude that Harvard is grade-deflating relative to BU.
* You're using average uGPA of LS applicants, but average high school GPA of all students. Those populations aren't necessarily comparable across schools. High-GPA Harvard people might be more likely to go to business school, while high-GPA BU people might be more likely to go to law school. Or a variety of other explanations.
* Your analysis is making various assumptions about the shape of the distributions of grades in high school and college. Even if both are normal distributions, if the standard deviation of grades is less in college than it is in high school (across the board), you would expect the difference in average uGPA to shrink even if no schools are grade inflating relative to others.
* There's also a reversion to the mean problem. Everyone's high school GPA is based on some combination of skill and luck. You expect people with the high GPAs who got into Harvard to have, on average, benefited more from the luck factor than the people with the low GPAs who went to BU. Since luck in high school is uncorrelated with luck in college, reversion to the mean dictates that the difference in performance between the two schools will probably shrink in the second measurement.
To make a convincing argument along these lines, I think you have to do something like what Berkeley did a while ago: look at students who end up at the same law school from different undergrads, and compare how uGPA correlates with law school GPA coming from the various undergrads. (Alternatively you could try to find a bunch of people from the same high school who went to very different undergrads, but I'm guessing the samples are going to be a lot harder to find that way).