If it's a garbage domain and the seller says they all of sudden have a bid that's $1000s above your bid, then let the name go.
If you're dealing with high quality domains, then you have to know what *YOU ARE* going to pay. If the seller goes beyond your price, then wish them good luck. Why do some people let their purchase price be controlled by others? That's a sure way to stray from your business plan.
Unless a seller is selling at a fixed price a sale is a negotiation! If you don't like the price the seller is asking or the offer the seller says he or she received, you have every right to break it off before you agree to a price.
High quality generic domains do attract a lot of interest in a very short amount of time. I have often had dozens of questions and offers within 1 or 2 days and some of them arrive via PM even if I've asked to post offers to the thread only.
Some buyers will never post their offers in public! The conclusion here is use your common sense and take responsability for yourself. Don't blame others for your own actions. You are the one after all who decides whether to purchase or not to purchase a domain.
That's not to say scammers aren't a drain on everyone, it's only to say that being careful and skeptical is one of the best ways to avoid being scammed.