Is it ok to use a "4-cycle only" fuel in a 2-cycle motor with mixed oil?

It is probably because the Tru-Fuel decreases the lubricity of the oil mixed into two-stroke gasoline.

2-stroke engines are on the ragged edge of utility because their lubrication is marginal. You do not want to do anything that might decrease the lubricity of their fuel; lubrication failure does this to a 2-stroke engine:

Low lubricity causes lubrication breakdown and failure between the piston, the piston rings, and the cylinder bore. The pistons, which are aluminum, scrape against the bore, which is cast iron and galling occurs (aluminum gets smeared onto the surface of the bore walls). Then the (cast iron) piston rings scrape off the galled aluminum which gets jammed into the ring grooves and causes the rings to bind and eventually to break to pieces. Now you have cracked rings in destroyed grooves and galled pistons, which quickly get jammed into immobility and the engine seizes. It is now almost completely destroyed.

I have been using the common (US) 10% ethanol gasoline in 2 cycle engines since it became the norm. No problems cause by ethanol ( in about 5 engines). I do have a leaf blower that won't run but no gasoline at all comes through the carb. I also use the ethanol /gasoline in 4 cycle engines.I have never used Trufuel , but it is difficult to think why it would not work as long as you put the necessary 2 cycle lube oil into it. Conventional 4 cycle engine oils contain ash forming materials ( zinc,calcium,barium,sulfur, etc) which should not be put into a 2 cycle engine.