According to Wikipedia, the story's a little bit different -- the Reagan campaign didn't ask to use it as a song, the Reagan reelection campaign actively sought to get Springsteen to endorse Reagan, pushed in large part by George Will, who had also penned a column in which he praised Springsteen as an embodiment of (conservative-friendly) American values based on Will's interpretation of the song (which did not precisely ignore everything but the "Born in the USA" line, but is if anything all the more strained for acknowledging the rest of the song but still holding on to its interpretation.)