'why are they doing that? Are they that desperate to sell her?'
I think it's a nice compromise. They probably know the BO or someone that works there, and are confident of the care, and are more comfortable doing that than having her tried at a completely strange and unsupervised location.
It's allowing the trial in a controlled environment.
Why are the doing it? Maybe they're decent horse people who want to make sure it's a good fit for their nice horse before committing. Maybe they realize her best market is as a first horse/novice horse and that first time buyers need a trial. Or maybe, like me, since they prefer to negotiate trials on horses they buy, they feel it's only fair to offer them on horses they sell.
The final reason might be that the market is very soft right now, and she's an older horse.
I think you can make yourself crazy overthinking this.
Don't take a horse on trial unless you can make good use of the trial time.