Okay, so I tend to agree with the argument made here... but hang on a moment. It's far from watertight.
So fine, it'd be stupid to say 'me tend to agree'; which does seem to lead to the conclusion that 'Jim and me tend to agree' should be wrong, and it ought to be 'Jim and I tend to agree'.
Right?
But who's to say that 'compound subjects' don't follow different rules? They're not exactly the same as singular ones; they're plural. It'd be equally silly to say 'Jim and I is right', or 'Jim and I am right' - it's 'Jim and I are right', right? (Or is it 'Jim and me are right'...?)
Have a read and see what you think.
Grammar Lesson - The Mistake That Bugs Me the Most
http://www.buildingpersonalstrength.com/2011/05/grammar-lesson-mistake-that-bugs-me.html