In the context of that sentence, "you and I" is the only correct grammar.
Or are you claiming that "me agreed with you" is proper
Your own link says that you're wrong:
Traditional Distinction Between “You and I” vs. “You and Me”
In order to see what’s changed, we have to understand the traditional way of differentiating these two phrase according to the grammar books. One thing is certain: You and I is not the same thing as you and me (similar case as who and whom).
Example:
You and I like our new neighbours.
Our new neighbours like you and me.
The convention says that you and I serves as a subject, and functions much like the pronoun we. On the other hand, you come across the phrase you and me as an object, just like the pronoun us.
So when I said "we" (meaning the 2 of us) agreed it meant "you and I agreed" because we were both the subject, not the object. To be the object it would be in a sentence like "He agreed with you and me.".
You didn't understand what was said in the link that you posted, and I'm not sure you understand it yet. You should stop trying to argue grammar with me. You are out of your league. What level of education did you achieve?