Thanks everybody.
Well the reason I assumed the trailer battery (which was the one stolen and replaced) had something to do with the brakes is that the brake paperwork had a warning that the *trailer* had to have a "fully charged battery" for the brakes to operate normally.
I'm to lazy to scramble out to the trailer and pull the paperwork to quote (though that's now easier since the heavy wind here shredded my rather old trailer cover) but if y'all are sure - and you sound sure - that there's really nothing wrong, I'll just continue to keep an eye on the brake adjustment.
And no, I didn't blame the guy, I asked here first. :-) 'Cuz you folks are so nice to an only partially competent trailer owner. Thanks a bunch!