My view would be if you're not monetarily comfortable putting something in the pay it forward forum, then you can't coherently say it's worth $0. If you say it's worth less than MSRP, then you should be completely comfortable selling it for whatever amount you say in the sell forums for that amount, to someone you don't have a personal relationship with.
If you have $3k MSRP of lights and you're saying that is worth $100 for the budget contest, then you are also saying you'd be willing to sell them for $100 to a random person on the forum or Craigslist. If you balk at that, and say no, I would only sell it for $1k, then you have your answer on what the cost is
My assumption being the thing to show/prove/disprove is the hobby can be done without deep pockets by a new person. That it's more about focusing on the basics then buying a bunch of stuff. An exhibition/contest where someone's using $7k worth of equipment feels kind of silly in a budget build contest, regardless of if they got it by being BFFs with a bunch of friends who give them free stuff.
An alternative way to follow this logic would be start the challenge with a flea market sale. Everyone bring all the equipment they're planning on using to a meet up, with the price they'd be willing to sell it for. Everyone can spend $500 on stuff, taking turns, and can buy their own stuff too. That's probably not what people would want to do, but that's the mindset that would be _fair_ IMO.