It is good that you admit they should have not stated things so definitively. However, mandating things was the goal, and that would have undermined that goal.
But you cannot claim that the statement "this continues to be a pandemic of the unvaccinated" is "completely true."
It is not untrue that vaccinated people were still contracting and spreading covid, and a even a
small number were ending up in the hospital and dying.
The statement clearly suggests (via the verb "to be", unless you want to go full Bill Clinton and challenge the definition of "is") that unvaccinated people are not part of this pandemic. This was false.
A thought experiment: Would you say the following statement is "completely true": "The AIDS pandemic in the 1980s USA was a pandemic of gay men and IV drug users"? Of course you wouldn't. But why not? AIDS overwhelmingly afflicted gay men and IV drug users. The odds of contracting HIV via male-female or female-female intercourse were extraordinarily lower in comparison to male-male (factually, this is a 1 in 71 chance of contracting via unprotected anal sex vs. 1 in 1250 chance via unprotected vaginal sex - nearly 18X the risk). You might want to think about why it is that you instinctually feel the need to defend these statements.
Something is either true or it isn't. You can't change reality. It can't be "true at the time" simply because you thought it was true. This would be like saying that it was "true at the time in the 1500s to say that the sun revolved around the earth" because that is how it appeared and no one could find evidence to suggest otherwise.