I know a lot of people, my sister included, who have a big issue with taking drugs prescribed by a doctor, but no issue with taking drugs purchased from a dealer. The logic can be pretty strange. For example I was talking with her about looking in to trying an anti-anxiety medication. My family all has issues with that, but she is far worse than the rest of us. My parents and I take low doses of SSRIs for it and it seems to help a lot. Thus it would probably be worth a try for her, since we have a great deal of genetic commonalities so the chances it works on her are high. Her response? "I don't want to do that, I only want to take the drugs I choose." I pointed out to her that it was completely my choice to take an SSRI, I could stop any time I wished, they aren't addictive, there is no court or medical order that requires me to take it, I continue to take it because I find it useful. Same reason we all take allergy medicine in the spring: It is useful in dealing with that, not because there is a requirement of some kind. She didn't like that though, to her it is different, though she could not articulate how or why.
I'm not sure why it is such an issue, perhaps because of the stigma associated with mental health issues, but I've seen it in numerous occasions. People who have no issue with recreational drugs that alter your brain chemistry but think that prescription drugs that do the same are evil or bad or something. It is, as you point out, a very silly position. I can respect, though not agree with, the position of taking no drugs that alter brain chemistry for whatever reason. However it is silly to be ok with THC and LSD and the like, but not with an SSRI.
Now please don't anyone mistake me for saying "Everyone should take SSRIs." No, not at all. However if a professional suggests they, or another drug, may be useful to treating a condition you have, you shouldn't say "No I won't take drugs," but then go out and smoke a joint. That is just silly. That would be like then refusing to use marijuana if a doctor prescribed it.