running the proper sized tube does offer more flat protectoin, the rubber isn't so stretched out, yes if you get like a nail or somthin in you rire it will flat no matter what, you also have a very small risk of just blowing out the tire if you hit it hard due to the shock and increased pressure do to decreased volume on impact, but you tube woudl have to be very close to just blowing out on its own.
running smaller then reccomended tubes is usually fine (exept the flat protection thing) however running a 1.25 in a 2.3 is pretty extreme, and I wouldn't do it unless i had no choice (as you did and you where fine so w/e) usually its people running a 2.0 in a 2.3 or w/e cause they changed tires or somthin but a 1.25 tube is just a tad wider than a road tire (also its on a 26" wheel)
one thing i've noticed when i've run tires that are to small in a road bike (usually if i run and 18-23mm race tube in a 28mm tire cause i don't normally run 28s) anyway when i do that it seems to leak air faster, and i've heard this from other people too, my understanding is that on a microscopic level air leaks through the rubber on all tubes, thats why you have to pump up your tires every week or so (or more often) with a too small tube the rubber is thinner so air leaks out faster and i had to pump up the tires more often. I've also noticed this on my mtn vs road bikes, the race lite tubes are thinner and i usually have to pump up b4 every ride to keep em at 120psi, on my mtn bike i pump em up idk like once ever 2 weeks or so, i also don't care about keeping a precise psi level on my mtn bike but w/e