Have a gander through a
project I did several years ago sawing my own veneer.
In my experience, "veneer" is wood that is <=1/16" HOWEVER, even wood at 1/16" can still move things. I don't recall if I mentioned it in the above thread but I had two 5/8" pieces of MDF about 16" x 36" that I sandwiched together. Next, I glued some of my shop-sawn 1/16" walnut veneer to one-side only and the next day, the walnut had pulled the flat MDF sandwich out about an 1/8" bow: from | to (. I was completely shocked. So the rule is to always balance the veneer on your substrate. Put the show stuff on the good side and the so-so stuff on the other side. As long as they are the same thickness, your substrate should stay flat.
Now I'm going to guess that thinner commercial veneer probably wouldn't have pulled the MDF sandwich out of flat. Just something to keep in mind.