"Type hints" are a very weak argument for "var", because they appear only when one places the mouse cursor over the var keyword. But when reading code, any professional developer processes whole lines and sections of code at once, without hovering the cursor from one var to another to find out the type (and remember it when the mouse is moved away). Hence I disagree with your idea that it makes no difference ... from reader's point of view - usage or non-usage of var has a significant influence on the readability, even in a powerful IDE like Visual Studio.
 Does that mean one should not use var, like your friend suggested? Well, this debate has already taken place years ago, on this site and elsewhere. The gross consensus is, there are several cases where usage of the "var" keyword does not make the code less readable, and several cases where it can actually enhance readability (of course, wrong usage of var can also reduce readability, that is also true). 
 Look into the older Q&A threads about this topic, like this one, or this similar Q&A about C++ and the auto keyword. None of the arguments in the accepted answers (and several other answers) mentions the IDEIDE's capabilities as an argument for var. So if you are going to argue for usage of "var", there are way better arguments than the availability of type hints in the IDE.
 
                