But what I would do to try to counter the rumor:
For co-workers I'm close with, I'd make sure they know why I was out, and make sure they believe it. Not by asking them repeatedly, "You believe me, don't you?" But throwing in some details about your illness, to bring home the reality & show you have REAL knowledge of that condition.
That way, you have people out there who will hopefully deny the rumor when it comes up.
Then if it comes up again around you, you could say that not only were you not in drug rehab, but you've never been in drug rehab or had a drug problem of any kind, and you don't believe in taking drugs.
Finally, I wonder why the drug rehab thing is the rumor. Are you known to use drugs or anything like that? The reason I ask is that, if I were out for 4 months, there would be rumors about why, but drugs wouldn't be one of them, I'm pretty sure. I'm not the type...it just wouldn't be what people would think. They'd probably think cancer, or complications from cosmetic surgery, maybe a family emergency. That's because I'm middle aged and a semi-vegetarian who has expressed a dislike of taking even aspirin...so no one would think I'm into drugs.
Here's what I did about maybe the start of a rumor once. When I got back from a long vacation years ago, someone remarked how refreshed I look, and she asked if I'd "had something done." I said no, but she said, "Come on...yeah, you did." I said, "I look that refreshed? I guess being off work really gave me time to de-stress. Thanks! But really...I'm the sort of person who would tell people if I got cosmetic surgery. I'm just that way." I think that was the end of it, as far as I know. And what I said was true.
I mention my breast lift I had occasionally. A couple of times someone has asked me if I had a boob job. That's odd because I'm not busty....well, not since I had my pendulous breasts lifted. I'm a C cup. What I said was, "Me? No way...not only have I not had an enlargement, I wouldn't mind being smaller. They just make me look fatter because of my chubby face and short waist. Not that there's anything wrong with people getting an enlargement." I don't know if they believe me or not. But they seem satisfied w/my answer. But if they don't believe me, there's nothing I can do about it. So I don't worry about it.
But there's no good way to combat the rumor mill. I think your best bet is to have several close co-workers out there who might say "that's not true" when someone repeats that rumor in front of them.