Old wives' tales aside, the ONLY differences between a 2-3/4" 1100 and a 3" model is the barrel, and the action sleeve. The receivers are exactly the same except for the rollmarking, and in fact so is an 11-87 receiver.
The barrel of course has a longer chamber on the 3" gun, and it has only one gas port, and the ejector button is a little farther back on the barrel tang so the 3" hulls clear the port. An 870 is the same way, but the ejector is not on the shorter barrel tang. The action sleeve is heavier on the 3" gun in that parts of it are not turned down as on the regular one. The gas pressure peak pulse with a 3" load would be longer, so you would need less area to admit the gas, and you could get the heavier sleeve moving to where it would complete the autoloading cycle without battering the receiver. I got this from Wayne Leek, the guy who designed the 1100, many years ago on an airplane. It is a 'balanced' design. The 11-87 merely used the "bigger" gas system and incorporated a method to bleed off excess gas with heavier loads so you can shoot almost any 2-3/4" or 3" load.
Remington sold/sells a 3" Magnum barrel that they advise only using with steel shot on a 2-3/4" receiver. They do not sell the Magnum action sleeve, so one cannot truly 'convert' a 2-3/4" gun. I do not know about all of them, but some of the early 3" steel barrels needed the gas port opened up one drill bit size (advised by Remington) to function reliably with the heaviest steel loads at the time. I am not advising anyone else to do it, but I used my 3" barrel on my 2-3/4" 1100 receiver with lead, steel, Hevi-Shot, and anything and everything else for 20 years with zero ill effects, but I did keep a very close watch on the recoil buffer.
P.S. - Tell your Popa that in fact Remington does still sell some 1100s that are 3". In fact they are made to shoot almost all 2-3/4" and 3" loads interchangably. Could be there's a little 11-87 hiding under that 1100 skin.
P.P.S. - Oops. Just remembered. An acquaintance who owned his own machine shop built up a regular action sleeve so the weight was the same as a Magnum one, so I guess he did fully 'convert' an 1100 to 3".