Hmm… I think the receptionist reacted precisely how I'd have wanted her to react if I'd rung up with the same query, and she has no way to know whether she's got someone with preferences more like mine on the other end of the phone, or someone with preferences more like yours.
Firstly, as you mentioned, when you're feeling low but just about holding it together, a kindly-meant inquiry into whether you're really coping can bring on the tears. That's something I absolutely wouldn't want on an administrative call to a receptionist, because I'd feel embarrassed, there would be nothing the receptionist could do for me in that moment, it might take minutes or hours after the call to rebuild my fragile able-to-cope framework, and I'd worry about holding up the queue.
Secondly, I've taken various psychiatric meds for most of my life, and if I'm bringing a matter-of-fact request like a consultation for a meds adjustment to the table, with no particular indication that I'm struggling, I like to be treated like any other patient making a routine request. It actually irks me sometimes to be treated with unwarranted gentleness, asked if I'm really truly coping, probed for suicidal thoughts, and so on, when I'm doing fine, presenting fine, and am there for something unrelated, or for some medication-related issue. I understand why they sometimes need to ask about my mental health, but I don't want to be automatically treated as inherently delicate and potentially less able to ask for what I need, just because I take medication for a mental illness.