Sorry, I do not know which countries attach your bike to your passport. Years ago, none did this. Now? Dunno. I believe it's still the case that most DO NOT link your bike to your passport. SO ... you can leave the country without your bike if you must.
Sometimes local govt. make it so difficult to get legal permiso to UN DO your TVIP or leave your bike, that some say, "forget it" and just walk away, leaving the bike behind.
The insurance coverage questions are for the insurance companies and IMO, some are simply criminal enterprises with official designation. Will they pay? Dunno. Some do, some don't.
But as you know, most countries require you to buy insurance before you are allowed entry with bike. Does this mean insurance co. will pay a legit claim?

Dunno. Don't get your hopes up.
Everyone has stories, so read up on as many as you can to find direction on this. Try to find locals in Columbia who know more about this ... see what they say.
Surly Colombian riders/drivers must cross into other countries ... do what they do. This true especially with commercial truck drivers.
Your questions are ALL good questions ... and should be made CLEAR if you are buying insurance. If they won't pay ... why bother getting it in first place?
Insurance companies will nearly always try to find a way to NOT PAY, using both legit and illegitimate justifications.
Seems to me, in just about every case you would need a good, local lawyer to represent you if you have an accident. A good lawyer will know how to deal with insurance company, the police and maybe even Aduana.