Sounds like a very obvious scam. Also, I hope you patented your idea first. If they just checked to see if it was patented and nothing came back, then that means they stole your idea and probably patented it themselves. So you basically paid someone to steal your idea.
It doesn't cost $1,195 to do a patent search. All it takes is a simple Google search of "Patent Search" and a few clicks of a button to search for a patent.
Ok well I would not do it if I were you. It sounds like they purposely put out the $8,000 figure and said "ok we'll pay half of that" so you think you're getting a good deal. When in reality, you're getting scammed out of $4,000. It's to distract you away from the huge amount they are asking for, and the huge amount they will take from you.
This company doesn't have any complaints with BBB, but they also don't have any history at all, since the company was just started last year. So they could be stringing their first victims along for a little while, or you could be one of their first victims. There are no credible reviews online or talk about them. Also, they are operating out of a suite, not a real headquarters. This is very suspicious, since they can basically pack up and leave and have no lease or anything to take care of, just a hotel room. They may not even be there, they may have just rented the suite out to make it look like they're there but are really in a different location so if they get into hot water nobody will find them. Then again, they could be legit, but my scam radar is alerting me big time that this is not a legit company.
You said you're not an idiot, and maybe you aren't. But I don't think a smart person would hand over 2 grand to a stranger and then later AFTER doing this, try to establish if the company is legit. just my two cents.