There is no argument here whatsoever. If someone says "meet you next Sunday", and the other person doesn't understand, then you will have to clarify by saying;
"this Sunday coming" or " the Sunday after". The use of "next" in the above statement is wrong.
To avoid any obfuscation, the correct nomenclature for the original statement should be either "meet you this Sunday" or "meet you Sunday week". It's all in the way we speak, people. The words are there to avoid confusion, and the English language is a beautiful thing. Use it properly.
I like the cut of your jib, man