Perhaps they are trying to reduce complaints of parts arcing and pitting the table, however there is some truth to their warnings, I do TIG welding on a 3/4" piece of aluminum, mostly stainless parts and once in a great while I'll get small arcs. I do clean the table top frequently to prevent...
I would use my 20 torch, you can weld some and then skip around to other joints to keep the heat input down if that's an issue. Also clean the tubes well as already suggested, 1/16" wall isn't that thin especially if you have a good fitup