That's certainly how I understand it, but I wouldn't stop being a woman if my neurological tissue was isolated from the rest of my body and migrated to a synaptic scaffold inside a life support system - and I don't think any other woman would either.
I can falsify your statement: I feel quite strongly that if my brain were put into a man's body, then I would be a man. I wouldn't be wild about it, and my personality would be quite quirky, having been shaped by X chromosomes, œstrogen, and a lifetime's socialisation, but I would rather live as a man than compromise my health.
I was curious about how others felt, so started a 'brain in a jar' thread on AIBU, and it turns out that 70% disagree with me, so your instinct was correct.