I think there's a little more to the two-stroke thing, especially with Toro. Blade tip speed is tightly controlled; ever wonder why you don't see those 32" and 36" single blade riders any more? Those 2-strokes are having a hard time making serious power at 2900 rpm in a 22" pusher, let alone holding up as long as the better 4-strokes...two-strokes just don't like to lug.
I don't remember ever using or even hearing about using "white gas" as a motor fuel, except the fellows that make those little model one-lungers you see at steam shows. When I think of white gas, I think of stove and lantern fuel, and I do remember buying it out of barrel up at the filling station when we went camping. That stuff was pretty much the lower flash point equivalent of #1 heating oil...burns clean, but not useful in an engine because there isn't any antiknock rating...probably around 60, good for a compression ratio of 4:1! I have some original manuals for a few old saws, including a McC 3-25 manual from 1949; they recommend regular gas (and the obligatory 30 weight oil)
Up until the late 1960's most oil companies rebottled and dyed plain-jane dino oils for use in 2-strokes. Castrol, Klotz and a few others began supplying bike racers much earlier, of course, but I think Shell or Sunoco was the probably the first major oil company to offer custom blended products to some of the OEM's. I believe Shell was the first major to offer a synthetic 2-stroke product, which was a boon to the boke racers, and a disaster for the snomo guys...the first stuff was hydroscopic, a real problem in cold weather!