Yeah, I think you're right that it would be problematic to double the fine on that basis. Plus, I just don't think that's how you handle it. Just because someone is "offering" something on TV doesn't mean they're going to actually do it - and you don't penalize the player for some crap on TV.
A better way, IMO, would be to pay attention for anyone saying that they actually did give money to the player. At the moment, I can't think of any violation of the CBA that it would implicate but there may be some language in there about fining "the player" that could give the league something to stand on - but I don't think it would be disciplined in the first instance. But I imagine the league would be able to take action (maybe even PA-endorsed) to have it known going forward that accepting money from another party to pay a league fine is prohibited.