A much more influential and respectful response could have been something like :

I have a totally different understanding of this. Can you please cite your sources?

I don't believe it's even slightly more likely a doctor would let you die to harvest your organs if they know you're a donor, much less "much more" likely. You have to be declared brain dead before you're even a candidate for organ donation, and I don't think that's a call that's just made offhand on the subjective opinion of a sole "decision influencer."

I also have these sources to back up my claim:

• Snopes
• MayoClinic
• DMV.org

To which I would reply :

You make some great points. Let me address some:

• "You have to be declared brain dead before you're even a candidate for organ donation" - The majority of organ donors are indeed brain dead, however it is NOT a requirement for unpaired organ¹ donation². The only requirement is that they have been declared dead. Some of the biggest reasons that donors are usually brain dead are:
  • Most other causes of death make organs unusable
    • heart/lungs/circulatory deprive the organs of O₂
    • Kidney/liver make the body toxic
    • infection makes organs weaker and would obviously be contagious
  • The 'Uniform Determination of Death Act' made brain death a legal cause of death in the US.
  • Legal brain death is not subjective, though sometimes is not true brain death. (More on this later)
• "I don't think that's a call that's just made offhand" - You are absolutely correct. In my experience, most medical doctors are legitimately concerned with the well being of their patients. However, specifically in hospitals, the entire process is clinical and utilitarian. Doctors do not have days, hours or sometimes even minutes to make life changing decisions all day, every day. Add pressure from above to support this $25 billion a year industry of organ harvesting and transplant and hospital culture (if not policy) and the scales can be tipped ever so slightly.
• slightly/

Source: Experience

^{1 Obviously paired organs such as kidneys or lungs as well as other body parts can be donated while the donor still lives.}

^{2 I can only speak for the US.}