This was recommended by author Terence Reese (and several members of the site).

But I was taught differently, at least as declarer.

That is, I was taught to count "trumps and honors." So, if you are declarer in a trump contract, with, say, 26 high card points and an eight card trump fit, you will be most concerned about the five outstanding trumps, and the outstanding five or so, of the 16 face cards in your opponent's hands. Assuming no overlaps, your primary concern would be over TEN opposing cards, not 26.

If there is a critical side suit in the play, you might worry about five or so additional cards in that suit as well. Then I have worry about 15 of my opponents' cards, but not all 26.

On the other hand, suppose you have a singleton, x in the dummy of your opponents' best suit, and xxx in your own hand. They start off with AK of the suit, and you ruff the second round. You've seen four of your opponents cards, and you don't have to worry about the remaining five cards in the suit (assuming that both follow when you ruff your last x). Then you only have to worry about the remaining 19 opposing cards. And of these, the most important ones are the outstanding trumps, and the two honors or so, outside their main suit.

Is this right, at least regarding a trump contract (no trump is a different animal)? Or is there something that I am missing?