So an American PPL (no IR) cannot fly "VFR" above an overcast layer?

In the U.S. "VFR on Top" has a VERY special meaning (in fact its not
really VFR and not necessarily "on top"). "VFR on Top" is a specific
ATC clearance. Flying over an overcast would be VFR that happens to
just be on top of an overcast

-Robert, CFI