Get a Stat Move From Another Playbook?

Many of the playbooks have moves that give them +1 to a stat (up to +3).

From the way I'm reading the rules, it seems like the improvement option to Get a Move From Another Playbook would allow a player to pick one of those moves, letting them raise a stat to +3. This seems strange since the improvements lists also include stat bonuses, many of the playbooks don't have options to pick certain stats, and many of the options that are there are capped at +2.

Is it kosher for a Gunlugger to take the Skinner's Breathtaking to get a bonus to Hot even though their stat improvements don't normally let them choose Hot? Or for a Brainer to take the Skinner's Breathtaking to get +3 Hot even though the Brainer's own stat improvement can't be taken if you're already at +2?

Yes.

Yup, totally kosher.

It uses up one of your 'pick a move from another playbook' options, which is a not insignificant price to pay for the advantages it provides. After all, you only get two of those, and there are a lot of good moves to pick from. Using the stat-ups in your own playbook has no such cost, and is thus still a significant advantage.