LMS FPS are as you describe, where it's all about knowing the map, positioning and the element of surprise. Those FPS only take a minimum amount of skill. Team based FPS have the opportunity for strategy and mind games much greater then fighting games. The use of decoys to lure another team into your trap, convincing the other team that you're going to one site when really the bulk of your players are taking another, or even tricking the players guarding a place that you're going to enter in through one door when you come in from behind them through the other door.
This is the reason that running makes sound and walking does not, crawling is possible, and objects like flash grenades and smoke grenades exist
All of what you are mentioning are team based tactics which are pretty damn hard to pull off with a team of 5 - 8 people and does take some skill. However, it still comes to the point of how to win. It's a shooter. It's not too hard to point, click, and kill someone. Yes, there are things you can do to make this more difficult however, once you learn the game you know all the aspects of what someone can do and it becomes very easy to kill someone. Look at all the FPS's played professionally. People don't miss very often.
I know exactly what you mean. I've played these types of shooters since age 12 and competitively. They do take very good team coordination and they do take skill. It's not like they are skill-less by any means. I just don't think they are quite as tough as fighting games. I wouldn't put them very far behind but IMO FPS's are still behind even RTS's.