This buyer will want to get in and see the property ASAP. Since they're so familiar with the market, they'll be able to tell once they step foot inside if it will work for them, if it's priced right, if it shows well, and if it's in line with present or past comparable sales. If the property meets their criteria, the real dealer, armed with all their knowledge and motivation, will make an offer.
The real dealer
Their offer may not come in within days of a property going on the market. But it will come from an informed buyer who is knowledgeable of the market. If a home is priced too high and a month or two goes by without an offer, it will be the real deal buyer who has been watching the listing and waiting to see how the market responds. If they note that there aren't any offers on it and there is no activity after some time, the real dealer will come in with a low offer, which actually may be a good offer, on the seller's home.
While you may see it as an insulting "low ball" offer coming out of left field, you should still look closely at this offer. Who is the buyer? How long have they been looking? Have they written other offers nearby? Are they working with a good local agent? Does the offer come with a pre-approval letter? Is this offer actually a number that is close to the number your real estate agent initially suggested?
As hard as it may seem to contemplate an offer much lower than your asking price, serious sellers should look at all the signs leading up to it and consider if this is the offer to accept. Trust your agent. And even better, trust the phrase, "The first offer is always your best offer."