“Free choice hay” is just a buzz word with boarding barns, and is rarely provided in reality. You self-care so I believe you about your horse as you’re in control of his feeding.
Every local barn in my area touts “free choice”, but it’s not unfettered access to hay 24/7. There might be hay in front of the horse at some point during operating hours. At turn in they’re usually given a few flakes, expected to last the ~12 hours they’re in a stall.
Boarders believe their horse is getting round the clock hay as peak riding times tend to coincide with feed times, and don’t see the hours at night or mid-afternoon the horses are standing around with no hay. Boarders have no concept of how quickly a flake of hay goes - about 30m. Do the math. That’d be at least 6 flakes of hay during stall time alone. Doesn’t include the other 12 hours a day.
Always look at the contract because many boarding barns specify “hay within reason” and then specify that is “3-5 flakes of hay a day” in their contract.
It is not economically feasible for barns to actually offer that service, unless it’s a roundbale or large (200+lb) square bale out in a field.
In other words, unless your horse[g] is in front of a round-bale 24/7, it’s unlikely he’s getting “free choice hay”.