Thanks to you all.
In the particular podcast I linked, Father Tom seems to go as far as to say that "discerning the body" cannot mean understanding that the bread of which we commune is the very Precious Body of the Lord. He seems to think this idea is scholastic and, while not outrightly condemning it, certainly condemns some of its knock-on effects.
That said, I might not have been giving Father Tom's podcast a fair treatment as I was listening to it while on a treadmill. In any case, I am not suggesting that Father Tom denies the Real Presence, but his seeming insistence that "discerning the body" cannot mean confessing the Real Presence seems odd to me.