You are absolutely right that if Pelosi turns down a $1200 standalone bill, then they hold the ball. At this point, she has not turned down that bill because it does not exist.
I guess I just don't believe that the Repubicans support that, even though Trump does.
Last night, I heard pundits say Republicans are not just against Pelosi's bill but any type of stimulus. For America's sake, I hope that is not true. However, Republicans hate government assistance programs, unless they benefit corporations.
This article below describes a scenario where Republicans and Democrats are equally opposed to it. Based on my research, I don't think we can put it all on Nanci. The Democrats have been trying to pass stimulus for months -- not just to help families, but to provide money for healthcare supplies, states, and educational resources. I just don't view Trump's offer as a good faith offer.
Passing a stimulus bill would make Trump look good but the Republicans refuse to budge. When they come back on October 13th, let's see if there is a bill from Republicans that is a standalone bill. If Nanci refuses it at that point, you are right. Until then, I think the jury is still out.