The Tristar and DC-10 were not originally used from La Guardia, in fact no widebodies operated from there for quite some years after their introduction.
When the A300 was being sold to Eastern Airlines part of the rationale was for it to operate out of LGA. It was still too heavy for some of the overwater taxiway bridges so Airbus, as part of the sale, paid for engineering work to be done to support the A300.
Once this was done the other airlines there who only had L1011s and DC-10s wanted to make a competitive reesponse to Eastern, and it was found that the mods that Airbus had paid for equally allowed the trijets to operate.
After quite some years of widebody service from there (though never 747s), deregulation encouraged the "smaller planes and more of them" approach to service. Nowadays I believe there are once again no widebodies operating from LGA, gone right back how it used to be.