The only thing unbelievable about Jason is how he's able to effectively reload all those Soviet and other shitty rusty guns the pirates have like a military soldier. Even if we assume he had some training it's unlikely he'd have access to EVERY gun he came across on those islands.
The rest? Perfectly fine. As
>>719953751 said, you don't start out super skilled. You have to unlock skills like skinning animals, takedowns, etc. Even within the "gameplay logic" it makes sense, so if we go with "it's just a videogame" it's reasonable to assume every time you unlock a skill Jason technically would learn this shit IRL, with his friendly natives.
And what
>>719953000 said is also true. Most of the people he's up against are bumbling retards who probably don't even want to be there. He's not fighting Tier 1 Navy Seals teams for most of the game.