I'm watching the episode "Safe" again and as the hill people bring Simon into town they yell out, "We got ourselves a doctor!" How did they know he was a doctor rather than just a rich dandy?
I never figured she did. But when a man engages in clandestine dealings, he has his preference for things being smooth.
Quick cut to the bushes shaking -- but there's no wind. Could it be hill folk baiting the schmuck?
She makes things not be smooth.
Right. I'm very sorry if she tipped off anyone about your cunningly concealed herd of cows.
MAL (guides Simon away from the corral)
I'm starting to think you got a little too much time on your hands, doctor. I think now I got a notion regarding that. Why don't you take your sister for a little walk.
Realize that this is a transcribed version, not the actual script, but that is the only indication that I can find where they would get the idea that Simon was, in fact, a doctor.
The clear implication is that someone (who we later learn to be the kidnappers, or at least their accomplices) were hiding in the bushes near to the cattle as the Doctor and Mal speak. Notably, Mal calls him "Doc", rather than "Simon".
In the original script, there was an additional (unfilmed) scene where we learn who was watching them:
MAL: What're you doing out here, Doc? Besides the scraping.
SIMON: I thought perhaps I could help. With the cows.
The last off screen because by now WE'RE UP INTO THE TREES, where...
... a figure, STARK, scurries away across the branches with an almost inhuman skill.
EXT. TREETOPS - MOMENTS LATER
Stark lands on a branch. Two other shabby men crouch there.
STARK: Got a good look. They waitin' fer a payment- Somethin' there worth takin', too. They got precious cargo.
The precious cargo is, of course Simon, rather than the cows.