Precisely. Though your experience may vary, I've had much more luck composing shots with the technique I mentioned rather than aspetto style photography ;-). (Wonder if that term has been copyrighted? Lol). Reason being though is that while remaining nearly motionless the fish will swim up to you, you are usually at their mercy to compose the shot you want since most movements will spook them away from you. Using the above technique lets you move around them without spooking them resulting in a much greater flexibility of shot composition (learned this technique from a number of really good U/W photographers. . . Cathy Church and Courtney Platt in particular). This also helps with the fact that if you wish to get full spectrum colors, assuming you are using a strobe, you need to be within 3ft of your subject or you can kiss the reds goodbye.
Meh, just one more tool in the box for those that may be interested in U/W photography for what it's worth.
Naturally, you are quite right. Physical contact should be avoided and if they are that close, unless you're using a wide angle lens, you're going to end up with a fisheye one way or another ;-).
Interesting. I've found swimming with them shortens the dive quite a bit, and maneuvering the camera while swimming with a mono fin is a bit of a challenge. Sometimes it is the best way to get a good picture, but it's not my favorite. I never use a strobe. I like the feeling of the natural colors at depth - that said, around here I am seldom taking pictures much deeper than 50 feet. It's true that when you are stationary you really have to watch how you move. I had a pair of small drums spook once because I moved my eyes! (the big ones come back and flare their gill plates to prove how badass they are)