Do these greenhouses need a permanent foundation?

For pop-up PE models, no, but anchoring with stakes or sandbags is mandatory or wind will roll them. For polycarbonate kits, owner threads are nearly unanimous: build a 2x4 or 4x4 wood base, level it, and screw the aluminum frame into the wood. Setting these kits directly on soil or pavers is the #1 cause of the 'it collapsed in a storm' complaints.