First.. a little 'disclaimer'. Different people will tell you different ways of skiing the bumps. On this board there are a few different 'styles' or techniques, which are different from each other. Bottom line - different techniques work for different people.
With that said, I believe you did get bad coaching. I say that because the more traditional way of skiing the bumps is in fact skiing the throughs (kind of). For the coach to tell you that skiing the troughs was wrong, when it was something that worked for you and to top it off.. that's the more traditional technique... it just doesn't feel right. I think it would have been better if the instructor said; "yes.. that is the zipper line technique, but I am going to be teaching you a different technique" or something like that. By the way.. I had a similar experience when I took my first bump class. The instructor taught us how to ski them over the top.. but I kept looking at the other folks skiing them fast down the zipper line and I kept telling him 'I want to learn that style' and he would tell me that was the wrong way to do it. After that class.. I decided to look for bump only instructors and that worked better for me.
To better describe it, you aren't really just skiing the troughs. Actually, you are skiing the throughs and the 'sides' of each mogul.. but certainly not the tops. Basically, you drive your tips into the mogul (not the middle of it, but to the side of the middle), absorb (knees up), roll over the mogul, and extend into and across the next through to the next mogul (and repeat).. all while turning with the knees (not the hips). I would say that the best technique is not a skidding technique (where skidding is used for speed control) since that can put you in a bad body position for your next turn, but one where the absorption and extension is what is giving you the speed control. However, skidding is a good way to control speed when you are learning absorption, or on big steep bumps where absorption/extension will not be enough. For me personally, I still skid on every single turn (unless it's a real flat mogul run) since my absorption kinda sucks and I am still a little scared of going too fast. But I know a lot of people that never skid unless it's real steep or real big bumps.. they also ski them super fast (boy.. do I want to ski like them).
That is the technique used by world cup skiers. It's what some people call 'zipper line' skiing. It's difficult for some and it takes a lot of time and dedication to learn, and that's why you'll see people ski the bumps other ways sometimes. However, if it's something you are able to do.. more power to you.. go ahead and do it.
I think often some instructors will not teach this technique, since it's a real specific technique mostly used by competitive bump skiers (although I do see a ton of people on the mountain skiing them this way) and some instructors might not know that technique that well. Usually the people you see skiing them that way are dedicated 'bump skiers'.. folks that pretty much only ski bumps, and instructors are usually more of 'all mountain skiers' and they apply a more general technique to ski the bumps.. with wider turns which would require you to go over the tops. It takes a long time to master.. and it often has you skiing (in general) differently than the all mountain type technique (for example, you turn with knee angle and not hip angle.. and you put pressure on the tips of the skis instead of just rolling the skis on edge).
To get a good idea of what that looks like.. check out these videos (and some of the material on the site). They are from a mogul camp website (I've attended a few of those camps). Two videos are 'Travis Mayer' (won silver on the last winter Olympics), and one if Mikko from Finland (another top world cup skier).http://www.mogullogic.com/lessons.html
also, for some mogul skiing 'porn', check this out (videos from the world cup)http://www.skidebosses.com/
Almost forgot.. another thought or comment. If your skis have a lot of sidecut, it'll be harder to do the zipper line. Mogul skis have very little shape to them (the 'rounder' technique is well suited for skis with a lot of sidecut). Also, as someone mentioned.. you don't want a super stiff ski either.