That would be extremely careless, and I find it very hard to believe that this happened.

An unlikely, but more plausible option to me would be that after removal of the Parler account, someone else was able to register the same account and gain access that way. But that doesn't fit the description all that well, and I'd also expect that this would not work at all if the authentication service is not very careless.

Maybe another explanation is that they quickly hacked around the lack of these services just to get things working again? I can imagine them quickly making a bunch of ill-advised code changes just to get their platform working.

Parler's infrastructure was extremely carelessly built in lots of ways, so it doesn't shock me.