It is true that Java runs GC periodically, and it is true that you cannot do anything while GC runs. But unless you have truly absurd operational parameters, GC will not take minutes to run. In fact it will be barely noticable. An example of how you could get GC to be that slow is if a runaway process caused most of your Java program to go into swap. Then when your Java program tries to run GC you have to wait as the whole thing is brought back out of swap as the GC run tries to access it.
If you're encountering that often then there are several things to fix. First and foremost, track down the runaway programs and fix them. Second, get more RAM. Third (if this is a server environment), get another server and split jobs up so that a single bad process doesn't screw everyone up every time. Fourth, consider running your server with swap disabled or (if your OS has such a notion) swappiness turned down. (That trades problems, it is easier to get out of memory, but memory pressure doesn't slow things down so badly.)
As for memory management, you're mostly wrong about that.
Being precise, it is true that the details of how the system handles swap and requests for memory are platform specific. However those details are hidden behind standard API calls like malloc/free that are very portable. Once you have memory assigned, it is up to you to track what used, which is application-level logic and therefore has every reason to be portable. When people talk about garbage collection algorithms they are inevitably talking about the latter piece, how within your program you track what memory is in use and what memory is not (and therefore can be reused without asking the system for more memory).
Therefore what people mean by garbage collection is very portable, and your basic memory management is likewise trivial to port. The exact behaviour of how that program behaves as you run out of memory will be very platform specific, but the code is portable.
As for his theories, unless he is doing something oddly stupid that leaks memory fairly quickly on each socket, he's smoking crack. It may well be that he saw some behaviour that he thinks his current practice solves, but I'd give very good odds that he misdiagnosed the situation and has developed a superstition based on an item of misunderstood experience.