It has nothing to do with tyres and everything to do with gears. The very first trials bikes produced back in the early 80's were basically modified BMX's and singlespeed so were ~110mm spacing. The wider 135mm spacing was used on mountainbikes to accomodate the cassette of gears to be used with derraileurs. When mountainbikes started being used as trials bikes, the rules stated that bikes had to have 6 working gears so the wide spacing remained and we had 26" bikes (stocks) with 135mm spacing and 20" bikes (mods) with ~110mm spacing. Note here that for the most part 20" trials bikes eventually went to 116mm spacing to allow for two 3mm thick snail cams to be used inside the frame for chain tensioning.
However, a few years ago, and due to the increasing trend for stock riders to run singlespeed for simplicity and weight saving, the rules were changed to allow singlespeed bikes with either wheel size. It was around that time that 'modstocks' (26" bikes with mod spacing of 116mm) were introduced. There are also a couple of companies who have toyed with 20" bikes with 135mm spacing ('stockmods'?!).
Anyhoo, think that's pretty near the mark.