Concealing your level bad sportsmanship?

[Sublevel27]

A friend whom I've played Munchkin for years just asked me "Your level is public knowledge, but how public is it?"

Primary question:
I really, really hate to ask the question, but our discussion went nowhere, so I need to ask: How public is a character's Level?

The reason he's asking is that he doesn't like using any Level Counters, because he doesn't like that people can see so easily his level. He likes to hide his assets as best he can, because he wants people to remember to ask him. He'll tell the truth, but he's counting on people not noticing, not keeping track, and forgetting to ask.

That doesn't strike me as Munchkinly, but rather poor sportsmanship.

I was surprised by the question from HIM because we both hate Rules Lawyers. I'm the GM, I own the games, I call the shots. So, I can just declare "Use the Level Counters/Level Playing field because that's why I got them."

Underscore to primary question:
However, is there any merit to his insistence on keeping his Level concealed unless someone asks, all because there's no rule that states he MUST display his Level for everyone to easily see?