If they charge money for the attendees/participants, then have them raise the price by one to five dollars per entry (Depending on how much you're going to charge them) and the budget for photography should miraculously appear.
Heres another one: If you encounter one of this many people who claim how much exposure you'll get by giving your work away for free (While THEY make money, of course), this is a guaranteed way to get them to put up or shut up:
You will draw up a contract describing the nature of the agreement which will go something like this:
You'll be more than happy to jump at the opportunity because the person who has made this magnanimous offer to you sounds like the kind of person who will scream about your talent from every rooftop imaginable, BUT:
1: They will pay your full rate. That is NOT negotiable.
2: For every PAYING client they send you (The referrals must come directly from the person who signs the contract), they will be paid a commission, percentage to be determined in negotiations.
3: The contract will be binding for as long as you are involved in that market, which will result in that initial client not only being paid back the amount they originally paid you to do that first job, but will continue to pay them for every paying client they send you. An annuity of sorts.
This is a great way to get the scammers and clueless to leave you alone. Not a single one of them will accept those terms, which instantly establishes their level of legitimacy. A legitimate businessperson would more than likely not even consider approaching a professional photographer in that manner in the first place.
Either of these scenarios are a Win/Win for you because you have either avoided dealing with a scammer, or you're going to get the job.