I understand what you are saying, but I still disagree. As Captain of a military vessel everyone on board is your charge. Having a foreign military vessel demand some of your sailors shows lack of loyalty and lose face to your own crew. On that note, it is also considered a criminal act to hand over troops/sailors to a foreign vessel without proper permission from you own military high command. Considering their warrant was signed by British MHC instead of US MHC it would have been wrong for him to do so.
As far as desertion, I do not think the USA commander, nor his crew would have felt the deserters were on the same rung as murderers considering they deserted one military to join theirs. Especially if they have been top notch crew members aboard your vessel (I am not saying that was the case, this is more or less in general). On top of that, the USA needed sailors for their fledgling navy so any experienced military sailors would probably have been welcomed.
Now I do not know what words were exchanged between the 2 commanding officers, and the British were in a state of war which makes unilateral decisions necessary, but the fact that they both didn't just pull into Norfolk's port (one of the US navy's HQ) and discuss it with the High Command seems silly. Sure the French where in port too but its neutral ground.
I am not saying the Commodore wasn't at fault (hell he was relieved of duty, though probably more for surrendering without a fight), but the British Captain is not absolved. Maybe they both fought in the American War of Independence as young sailors and still had animosity towards the other, or maybe the American officer was too arrogant and the British officer was too hot headed, regardless this could have been resolved without a shot fired.
I think it also came down to the feeling each country had for the other at the time. USA didn't feel like their sovereignty was really recognized by the UK and they were being trampled on. I can't say how the UK felt towards USA at the time. Oh Napoleonic Wars, how crazy it was.