As I said, I am new to match play, so maybe I am missing something, but it sure seemed like they were conceding too many putts to each other. Even the TV commentators mentioned something on the 19 hole, where they conceded each other's putts, even though one was 3 feet and change, the other was four feet and change.

Why would you concede ANY putts in match play for that matter??

You can concede as much as you want. Some do it as for strategy reasons. Say a guy is on the 7th hole and he has not attempted any putts under 3 feet, you might want to concede and keep his short putts on ice until later in the match. By then he won't have the feel for short putts and might miss an easy one. There are many stratigic reasons. Some do it for respect purposes. I've never been a fan of the concession, just putt it out.

Some people expect one, two or 3 foot concessions and if you don't give it to them, they get worked up over it and it sometimes throws their entire game off.

Sometimes when I play with friends, to speed up play, (Especially if is crowded on the course that day) we will concede putts that are the length of the putter from the hozel to the grip. Roughly 2 1/2' (Most of the time though I need to hear the plock-plock of the ball in the bottom of the cup) There is something satisfying about that sound!

I think some of the putt "concessions" have become much too common in pro golf. A three and a half footer with some curl is a missable ( is that a word ?? ) putt by anyone. ANYTHING four feet and beyond should never be conceded.....unless you have the guy or gal by the throat and THEY are buying the beers later.
There is a kind of etiquette involved between these guys that has gotten out of hand these days. Anything in the 1 or 1 1/2 foot range should be conceded , but i would not concede anything much longer than that.

I think they conceded putts that were longer than tap-ins. The match probably would have been over much sooner if they forced each other to putt everything out.