It's not Tallis Scholars you're thinking of, it's Pro Cantione Antiqua, Bruno Turner's group, that did it down a 4th. That was a common transposition for pieces in high clefs (treble top, tenor bottom).
I did this for a wedding mass summer before last, and I had to grapple with this issue, which was complicated by the fact that he also wanted the Laetatus sum from the Monteverdi Vespers! People are used to hearing it high, and it has a different affect that way, even though I think it sounds better low. So we found 4 high tenors, plus sopranos to match. Down a 4th, you have 2 normally-low bass parts, 2 baritone parts, 1 high tenor and a top part that anyone female (and some males) can sing.