Unless you're doing doughnuts, have your tire filled with nitro and blasting caps, or have it massively overfilled, it's not going to 'explode'. Even with sudden complete failure it's gonna be fairly undramatic unless you're driving at a good clip. I've shot the tire out on a car before (rural texas, bored, was taking the car to the pic-a-part anyway), and it just fizzed and went flat. I've also had tires completely blow due to road debris at varying speeds over the years, and pretty much anything below 40mph isn't even remotely dramatic. At speeds of 70+ it's a little alarming though. For common sense, driving at low speeds with such a tire is no big deal.
The companies and general wisdom have it as a rule because in all probability, the fix won't hold for long, and when it fails, it'll fail quickly, making it dangerous at speeds. To make things more intense, it's much more likely to fail when there is greater pressure on the sidewall, such as during a turn. All of this adds up to the lawyers saying the obvious : don't fix sidewalls. Which is great advice for almost everyone, because most drivers do indeed need their vehicle to be usable above 40mph, lol. It'd be even worse if you fixed the tire, forgot about it, sold the vehicle to someone, and then they had an accident doing 70mph down the interstate.
All that said, under very strict circumstances (driving slow, rural duty, temporary), it's not exactly juggling hand grenades.