This just happened to me on the green of the last hole.
I played a Tour Pro with a 63 average and started quite badly and, as I’m also not very good at putting yet, was at +2 vs -1 after 2 holes...
I slowly came back, though, playing secure shots, and the game was tied at 0 on the last hole.
I reached the par 5 green in 4 shots, he did in 5 (he was closer to the hole). And he left! Considering that I’m average at puttin, he could’ve gotten back.
I was a bit surprised, as he seemed quite friendly.
I quit once only, when my baby woke up and started to cry. It was even before the first tee shot! I apologised and left.