That's because as it states in the second paragraph the FAA only requires it be proved that it can maintain/climb at 5000ft and not exceed engine limitations on a 100F day (that being 100F at SL). The limitation would only be imposed in the limitations section if it had a temperature limit that curbed it's performance below FAA certification limits. Piper then provides no guarantee that above 100F SL temps that the aircraft will perform, so the pilot is entirely responsible past that point.
The Chieftain flight manual offers absolutely no advice on what the operational temperature limit is. The normal take off chart only goes to 35°C and the single engine climb to 37°C, yet the performance section preamble says for single engine climb at 38°C (100°F) increase climb speed from 106 to 110 kts, if you encounter 38°C at altitude then logic says the ground temp is higher than 38°C.
That statement is critical, it says "until on a 100F day" that does not say beyond a 100F (37.7C) day. One that means we only cover the performance data up to 100F (37.7C) at SL, beyond that you do not even have the IAS to maintain engine limits, but it will be higher than 110Kts. That is we did not test it beyond that, good luck, have fun, you are on your own if you crash. So two things at play here, you are having to increase speed to MAINTAIN cooling of the powerplant, higher speed means less climb, and also the density itself will reduce performance. BTW 37.7 is the critical temperature, as 38C is beyond the stated figure.
Again its a liability issue, not so much a legal limitation issue, you will find out if you are correct when in court, which as I said earlier has already been tested in the US and Piper has already made a statement that the lines are the end of the tested envelope so they hold no responsibility for performance beyond that.
I'm not up to speed with FAA certification, but there's probably a reg about operating outside of certified performance criteria, so if piper was required to test within an environmental envelope, then that envelope applies, without them having to state it as a limitation. Maybe that's where a firm answer lies, or maybe the regs allow you to make your own decision and generate your own data should you wish, at your own risk of course.
PS from what I read on US sites the FAA gets you under 91.13 or 'reckless operation of an aircraft' if you crash due to lack of performance at high temperature. Which is usually combined with being overloaded for the conditions.