The man who apologizes is the bigger man.
***
In the case of someone who has genuinely done wrong, yeah. In this case, definitely yes.
Of course, if the media starts demanding you apologize, the correct answer is usually to double down because you’re probably right.
The media will sometimes jump on something wrong you did. That doesn’t mean you need to say your sorries to the media like they were your moral auditors. In a case like this Cruz could have issued a separate “classy” statement and then referred questioning media to what he had already done without further comment.