While it's possible there are also a ton of possible causes for only being lame under saddle. Some of which have been mentioned. My most difficult one was a mare with navicular. Navicular can come on slowly and gets worse after work or with increased weight on the horse. Then it may go away after the horse is turned out for awhile. The mare seemed to just be lazy and not want to move out. In the pasture she'd run around with the rest. She never clearly limped because she was evenly lame on both sides so she just walked slowly to avoid the pain and refused to do work. Every spring she'd be worse than she was last summer. Over and over again the vet said she was fine. Eventually though a spring came where she just would not do anything. Finally after another round of xrays we saw the problem. Xrays also don't always show the start of mild navicular. That year was her last. She went downhill fast and despite injections into her legs, corrective shoeing, and everything else we could think of she was unable to walk by that winter.
I also had an older mare that I think contracted epm. The symptoms of this disease are highly variable so it's hard to say and we didn't have a vet test her. She was fine one year and the next every time a rider got on her she'd stumble and refuse to go beyond a trot. Being old, lazy, and incredibly smart (one of the smartest horses I've ever dealt with) we at first thought she was trying to get out of work. Again though it got increasingly worse until it was obvious something was wrong. Unable to find any real cause at the time we figured old age and joint problems. We gave her away to a family that just wanted a pasture pet the kids could sit on.
A third example... There was a small gelding in my college class that I was assigned to along with another rider. When asked to turn he would refuse and start limping in the back but was fine in the pasture. Another lazy horse that we thought was acting. One day I went to saddle him and when I tightened the cinch he flinched severely. I pulled the saddle, went to find my instructor, and she checked his back over. She thought maybe it was just some scrape he had that was upsetting him. Eventually I asked for a new horse because I hate lazy horses. I like running barrels and speed events. A week later his other rider came to tell me they'd had a chiropractor check him because after I brought it up they'd watched him more carefully while saddling and found he flinched nearly every time. His back was out of alignment and after some work he was like a new horse. Extremely active, ready to go, and no longer required spurs or a crop every other stride.
More times than not there is a real problem behind the lameness. If it were me I'd start by hopping on bareback and see what the horse does but then I grew up with an ornery pony and no saddle so bareback is no problem to me. Otherwise I would get someone out that really knows tack fit to check the horse over. Then also have some flexion tests done after riding. Your vet should have done these. You bend the leg into various positions and hold for so many seconds then try to trot the horse out. Usually in a straight line but sometimes on a circle. If the horse moves uneven or is harder to move out after bending the leg it's likely a lameness issue in the leg. It helps to do these on concrete where you can hear the even or uneven gait in the foot falls.
