Can we apply to the admin for this "Trusted for Escrow" Badge?
You can ask him directly.

Of course there were different deals between forum users, but how do you expect to find information about that if most deals are made via PM or so?
Escrow is the meaning Third party , right ?
If every trade via PM and make deal trader member A and member B is the meaning "P2P" , and that's no need for "Escrow" or member C for trading member A and member B, this is only my mind and if i'm wrong , im sorry . 
I didn't follow this too closely so I know just few cases when there were deals between forum users, all cases I remember were without an escrow. But it doesn't mean an escrow was never used. There is even
the forum escrow service, so probably there were some deals... or not.

I know there is no reputation or flag here, but at least you also have to give a sign of potential danger to some accounts that teleport. If on the btt forum he is quite dangerous, it could be that here he has the potential to carry out other dangerous actions.
I'm sure, no one agrees to be a victim of digital crime here, therefore, if there are no red or negative flags then applied in altcoin talk, at least there is a special badge for members with a bad reputation when teleporting. That's just my suggestion.
I am not comparing features between forums, but only intend to prevent unwanted bad things from happening here.
What you suggest is to trust blindly some third party. If all tags on BTT were 100% reliable, it could be reasonable, but we all know that there is a bunch of tags based on political disagreement, some strange tags like "I don't know this guy, but he left me a negative tag, so I'm doing the same", many tags with insults without any references, etc. It doesn't look reasonable to take all that mess of good and bad tags and blindly take here, but I don't see anyone who is ready to make a work on rechecking the facts behind those tags to take here reliable ones only.
If you have an exact case of some teleported scammer, which can be proved, please share your info.