The second part is indeed wrong: most consumer energy markets have a wholesale market and grid operator, and the grid operator is ultimately responsible for the call on brown-outs. The companies that sell electricity retail to invididual homes are generally buying on that wholesale market, but they're not in a position to cut off their customers: there's straight-up no mechanism to do that on a moment's notice, because the grid-level control doesn't overlap with the retail seller's customers (these retail companies are often basically just a financial instrument that turns the combination of variable wholesale and grid operator fees into a fixed price bill and some customer support: your neighbour can buy from a completely different company and if anyone wants to shut off you but not them they need to come to your house and physically disconnect the lines). What happens in a situation like texas is that the retail companies who are selling at a fixed price start losing money fast, and can't really do anything about it in the short term. If they've built up enough of a buffer from their margins, they may survive, or they may go bankrupt and their customers will need to move to a different provider, but that's a process that takes weeks to months, not minutes in a price spike.
(A similar thing happened in the UK: there weren't any brown-outs, but the spike in wholesale energy prices sent a lot of smaller retail energy companies under. If you were with one of them, like I was, you had no interruption to your supply and in fact won out compared to those on variable tarrifs: the losers were the investors in the retail companies and those who they were unable to pay).
I will agree in general though: unless you have particularly unusual energy consumption habits, or think that the energy market will go up more than the retail companies thing they will, you'll probably win out on a variable rate contract over time, especially if you have a battery to time-shift your consumption (And with the most common UK provider for this, there is still a cap on how much you'll pay, even if wholesale prices skyrocket like they did in Texas).