There are two reasons I can think of why that wouldn't happen: first, there's no primer to even initiate the reverse transcription. Maybe you might get unlucky

There are two reasons I can think of why that wouldn't happen: first, there's no primer to even initiate the reverse transcription. Maybe you might get unlucky and there's something close enough floating around. But integration machinery usually requires some specific sequence to identify the ends of the viral genome. Maybe that exists, it's not my field, but I've never heard of one. Also, even if it did integrate, there would be no promoter, so the vaccine gene wouldn't get expressed. So the only danger I see would be if it integrated into something functional, but the virus was going to do that anyway. But this is so improbable to begin with I wouldn't worry about it.