Two Truths and a Lie

Ike hid new submissions tip not out hopefully IOU I'll still pad fur end sew it fat enough fox tie competition! From Gus

Wok! She twist has so dew any fan! I mad to go over it ail again at tie and just to sew what I hid wrong. Tea but of men!!!

Having every three-letter entry in the grid feature two "true" letters and a "lying" one is a brilliant concept. But since 1a is FOE and 1d is YES, I’d have thought that the rebus FY belonged at the crossing, Y being the lying letter in 1a and F, the one in 1d. Instead, it seems that the solution is H because it’s lying both ways (while producing HOE in 1a and HES in 1d). Okay, but why can’t it be R (ROE/RES) or W (WOE/WES)? For that matter, why is there an E at the crossing of 9a's BET and 11d's DON (forming BEE and EON) and not an N (BEN/NON), an S (BES/SON) or a Y (BEY/YON)?