They also do insist on having their own grid - separate from the rest of the country.

It's true, but they are able to buy and sell power from the eastern grid (my understanding is it's less efficient, because it goes to DC and back to AC at the interface, but it does happen normally). They weren't able to buy any power a year and a half ago, because the eastern grid needed theirs for the same winter storm, but presumably during summer heat waves it works better as long as points north aren't all running their air conditioners nonstop as well.

The low natgas line pressure was also related to the fact that points north were using more than usual as well. In fact, one of the responses to the power outage was to stop all natgas flowing from Texas to Mexico. So it's not only the power grid, but also the natgas lines, that connects Texas to points outside.