the problem with your argument is that 'enemy of the state' wasn't a very original movie to begin with...yes it's possible that someone saw its success and said 'hey let's piggyback on that movie's popularity', but it's not very likely, IMO

as someone has already said, 'enemy of the state' had more in common with films like 'the conversation' or 'blow up', which wasn't quite the same thing as what the bourne story was

i'd say it's more likely that spy movies inspired the producers to make the bourne movies...james bond, perhaps, or maybe even 'spy game' which came out before bourne (*checks allmovie to make sure*)...'spy game' kinda had that hyper-editing, european espionage setting that bourne had