I have spent many years LECTURING differential and integral calculus courses, up to MSc level. I am talking here about the laws of reflection and how they apply to randomly positioned reflective surfaces, which has nothing whatever to do with more advanced mathematics. Maybe you could give an authoritative reference to support your comment, but I wager not.
And I can assure you that no way is a bit of Al foil going to be able to bring infra red radiation to a focus. Which is what is needed to create a hotspot. If you were to take the parabolic mirror from my Maksutov-Cassegrain telescope and very carefully position it between a heat source and a plant you might JUST be able to bring heat rays to a focus and cause a hot spot. But a piece of randomly crunched up (or not) Al foil - no way.
So go on using Al foil if you want, guys - this IS an Old Wives Tale. You will NOT get hot spots
I'm by no means a math professor (I'm in CS, just dabble in math), so I would easily defer to your experience. Not going to attempt a proof, but there's a proof of at least a part of this in var-pur-rig calculus with diff equations, 9th edition, page 511. Not precisely geared toward this because they are proving the optical property of the focal point, but this can be morphed toward what I was talking about...
anyway, I agree with you, the odds seem very remote (something I stated several times), but that's different than saying it's impossible.
In a way you are kinda making my point. The odds are remote, but they exist, and given enough trials, it certainly can happen (I honestly have no idea of even the ballpark chances that you could create this, since there is no way I'm going to try to work the math on exactly what it would take given an energy source and proper shapes). I also pointed out that given the likelihood of creating such a situation, worrying about it is silly. Kinda like worrying about a meteorite hitting our earth and ending our lives, quite possible, but rather unlikely during any one persons lifetime.