Yes, this does show some shortcomings! It's not the first time though! A Cessna 150 was reported completing a circuit with a pail of concrete hanging from the tail. I guess that C of G envelope is a bit bigger than the book says...
The Cessna flight manuals sometimes make reference to a minimum of 700 pounds per tiedown for adequate restraint. I'm sure a Piper would be similar. If the 700 pound restriant were to be used, this would not happen - the plane would never move, much less get airborne!
Doggie screw in tiedowns did not hold my dog, I certainly would not trust them for my plane. I've seen several planes on their backs, still tied to these, whose spirals still held bits of sod!
Pilot DAR