Vance,
What you are saying is nearly all correct.
Only problem is, you're basing everything on dollar amounts. Of course money is very important, but it does not mean the same to every single person.
My belief is as follows...
The player who truly wants nothing more than to play baseball (no right or wrong), should sign when the opportunity presents itself.
An arguement could be made that the player who would sign for nothing is the one that is doing it for the right reason.
If the ONLY reason for signing is the amount of money... I don't believe it's for the right reason. In fact, it might be a recipe for failure.
There are many sides to this debate. I don't think there are any standard answers that fit everyone.