"If someone had a physical imbalance of neurotransmitters and/or receptors in their brain, would that be my fault?"
Um... no. (:
The only thing that COULD be "my fault" would be... a lack of empathy. And, ironically, "thinking it's my fault" would not only be narcissistic as fuck, but would also display a pretty much COMPLETE lack of empathy.
I wouldn't think it was my fault, no. Now if she seemed to become MORE depressed in the relationship then I might think so. But generally people who have depression are gonna be depressed no matter what.
No, I wouldn't think that unless they told me it was me specifically. Depression usually isn't brought on by any one thing. It's a plethora of events and people and things building up into one giant ball of ickiness.