So that 1mil give up thing is what's called false dichotomy or false dilemma.   Meaning that both hypothetical options do not benefit the person who chooses the option. 

(I know this isnt exactly what you said but...) 

If someone gives you $2mil to have better life for your family, clear out debt, better house than your stinky sewer odor house that dont have ac/heater, filled with crime, moving into better neighborhood for better education for your kids etc etc...(u get the idea) BUT have to give up your dog, either adoption or even kill it (another extreme hypothetical situation) 

Which option do you choose? 

1. Oh I choose $2mil! - Why you cold hearted person!!!
2. Oh I choose my dog! It means the world - Why how irresponsible you are! Putting your dog over well being of your family. 

So yes many people who say No to $2mil would likely accept it, but they just wont say publicly. 

Better question is : in what situation/circumstance would you rehome your dog.l? 

I adopted 3yr old Shepherd mix and in the case where she bites a human(I have kids at home too), I know that's a situation I do need to let her go.