Wasn't most Mexican territory in the far north claimed in name only? No actual Mexicans were living there, at least not inland. Political control was hypothetical. Americans moving into Texas were opposed, but people moving into the OTL's Utah (whatever it might be named in this ATL) would be relatively free to do so.
Oregon was much the same. In the OTL, oth British and American citizens moved there. If Moromons or some other group moved all the way west into Oregon, the British would hardly be in a position to stop them. The presence of more Americas might even weaken the British claim, leading to all Oregon being entirely American later on.