Home Depot and other home centers have some people that do not know their heads from a hole in the ground and actually have no skills in the areas that they work.
when labor was hard to come by, and there was an opening in the flooring department, they would hire a warm body just to work there. This person could and would say anything. I know there is very little training in these home centers.
Now, the lino has to come up. There is no way tile could go down over lino. It will come up with those tools. You must get it all up or the tile will be uneven.