The point is that too much power is too much power regardless of the shape of the waveform!
Since most people try to "match" their amp to their subs or even run amps capable of doubling rated power to their amps the extra 30% power whether clipped or unclipped puts you from a safe operating condition into trouble really fast. The logarithmic dB scale and the way acoustic power works makes this even more of an issue.
Let's say your volume is at 22 on your head unit and you can bang away all day long, your amp is making 5000W. Now raise that one click on the volume knob and you're making 7500W. Your coils that were right at their limit at 2400W each are now way beyond that. Now raise volume knob another click and the amp is trying to make 10KW.... make that a clipped waveform and it's making 12-13KW. Even forget about the volume knob and substitute the wide dynamic range of music. The same example with you playing a 1000W amp and I'd wager it would be virtually impossible to blow those Z's even with a full square wave. My 0-35 Kenwood is right about 1 click = 1.4dB and once you get higher and higher compression ensures even less than that actual output for the power you're trying to throw into things so essentially in the space between what feels like just slightly louder you go from perfectly safe to get ready for smoke.
Clipping is far more strenuous on the amp and sounds like dirt is why we avoid it. From the sub's point of view, current creates heat and too much is too much. Again, take a 12" sub next to an 18" sub same motor and suspension and correctly proportioned box/port and tuning and play a 30hz tone and watch how far the cone moves. I'd be willing to bet it's more than 30% difference which your theory suggests is the deal breaker with "dirty" power.
Does your "clip" indicator light sense voltage, current, or a product of both? It's highly unlikely it's actually examining the waveform and is likely just going by some theoretical "max" voltage.
So, back to OP's post, he has a 800W sub that he is throwing 1300W into assuming he's hard clipping his 1000W amp. I'm very confident a nice round looking 1300W sine wave would fry that Alpine sub just as quickly.