Here are some interesting stats. There are 1716 unique pair vs. overcard matchups. That's after eliminating equivalent hands, i.e. 6c6d vs AcKc is has the same

equity as 6c6d vs AdKd, which is the same as 6h6s vs AsKs, but not the same as 6c6d vs AhKh. Pairs have an advantage in 1435 cases, and a disadvantage in 281 cases. The maximum equity for a pair is 57.5% for 8c8d vs Ah9s. The minimum equity for pairs is 46% for 2c2d vs JhTh. The most even match is 3c3d vs AcTc with an equity of 50.007%, a mere .007% from equal.

I suppose it's a bit late, but as far as the OP question, I don't understand where 32% comes from. Here's a rough calculation. Preflop there are 4 cards missing from the deck, leaving 48. From those 48 we have to choose 5 for the board (flop+turn+river). As you say, 6 of those will pair the overcards. Suppose they don't pair? Then all 5 board cards must have come from the 42 cards which don't pair the overcards. Thus, the odds of NOT making a pair are (42 choose 5) / (48 choose 5) = 850668/1712304 = 49.7%. So the odds of making a pair are 50.3%. Of course this completely ignores straights and flushes and the fact that the pair might also improve. Which is why the exact numbers vary as above.