Is your mental model of the pardon process actually confused? Yes, the president can unilaterally issue pardons, and Donald Trump is president until the end of his term, so he can issue pardons on his last day in office.
The comment was about last-day pardons, not pardons in general. Its a topic many presidents have gotten flak or attention for.
edit: oh, I guess "and Donald Trump is president until the end of his term" could come off as patronizing. I meant it just as a statement in a chain of reasoning
Arguably, if you impeach someone in public office, even if they aren't convicted by the Senate, any pardon of those same acts becomes moot and they can be tried in court for the same offenses. At least, that's what the DoJ suggested in 2000.