That will be the reason why. What is meant to happen is that the Paste menu item has the Cmd+V shortcut. So when the user hits Cmd+V, it's that menu item that activates. It's tied to first responder, so it sends the paste message to the first responder pseudo-object. This triggers a paste message propagating through the responder chain.
Really you should have an edit menu. Users expect it and it's the easiest way to make Cmd+V work.
If you refuse to have an edit menu, then you'll need to add manual keyboard event. Read the Cocoa Event-Handling Guide, in particular the Handling Key Events chapter, but only after having read the first 3 chapters.