It's the first time I hear something like this; if that's true, then this must be one major case of meaning shift, because since forever I've known and used and seen used this term to refer to the flaws of privatization. The solution to tragedy of the commons is literally a central authority. It's, like, the opposite of "driver of privatization".

Tragedies of the commons are often aimed to be 'resolved' through central authority, but another way of stating what's happening there is that they are being resolved by someone being granted the ownership right over the commons (in the cases you're mentioning, government). Therefor, it hasn't exactly meaning-shifted, but 'contextual' implications of the term for the reader are definitely bimodal with respect to privatization.

Tragedy of the Commons was specifically the idea that cooperation would fail due to selfish competition, so some force was needed to administer it.

Economists used it to argue both for privatization and against, but always for top-down, authoritative control.

In the US, it was almost always used as an anti-"socialist" argument for privatization, by arguing that the free market would in fact be an analogue for the "natural" competition, because as we all know the Free Market always finds the most equitable and consumer-desired outcome.

I'd imagine in Europe it was more common to argue for government management.