It's a very reasonable argument, but it's not logically airtight.
In general, it's dangerous to presume that just because Bob believes idea X, and idea X leads to idea Y, that Bob can/does/would/should also believe idea Y.
You have to make assumptions about what Bob knows, whether he knows the connection between X and Y, whether he would agree to believing Y due to its logical relationship to X (i.e. is Bob willing to accept logical relationships? should he be?)
So you can't prove someone else's state of knowledge or hypothetical state of knowledge based on the connection of ideas without assuming some things about the ideas in their head and the rules for how they combine those ideas.
Let me give you a sample argument that may illustrate the looseness of Q20's:
Anyone who insists that Yogurtland serves food should also agree that Yogurtland serves something necessary for survival, since food is necessary for survival.
Sounds logical enough, but I don't want to agree with that.

Hope this helps.