Both realize that this was an attempt to play to the media and embarrass Pence.
Trump told the truth and said that it was disgraceful and demanded an apology.
Pence chose to shrug it off and try to diffuse the situation.
It remains to be seen which approach will work better. Is is better to ignore the deliberate and dishonest attacks and or is it better to immediately refute them?
“I will leave to others whether that was the appropriate venue to say it,”
Exactly. So many entertainers and others today have terrible manners and horrible public decorum (no sense of appropriate boundaries in speech and behavior).