The charges aren't "bribery"; they're fraud - two counts of wire fraud and one count of conspiracy to commit wire fraud. Those crimes require a victim (or at least someone to be defrauded).
More generally, I think the bribery-is-illegal argument is somewhat overstated. First, I don't think there's a federal crime of bribery. (Indeed, the DOJ has had huge problems recently prosecuting even pretty clear cut political bribery cases precisely because the law around this is so unhelpful.) Second, even to the extent bribery is a crime, you have some more definitional work to do. Just giving someone money to do something is not bribery. When I was in law school, law firms bought me dinner and (a lot) of booze to encourage me to join them. Those weren't illegal bribes, but they were certainly giving me stuff to do something. Similarly, if I offered a neighbor $1,000 to attend my alma matar, that wouldn't be an illegal bribe (and certainly not a federal crime) but it isn't obviously different than what these agents were doing.