Actually, that's exactly what you want to see. If true, it would make the lounge a better-run place. Which do you think would be better: have the manager work the front desk (along with other positions) at least part of the time, so they know exactly what is going on, or to have the manager hide in a back office?

But, there's a better question to ask in such situation. Instead of asking for "the manager" or "a manager," ask for "your manager." This way, even if the person you're dealing with is a manager themselves, you're still requesting to take it up to whatever the next level is in the hierarchy. They may in fact be the duty manager, in which case you've reached as far as you can, at least on-site and at that point in time.

It reminds me of a situation that coincidentally I happened to observe in the TBIT check-in area. There was some disagreement with a passenger and a particular personnel (he may have been a line-minder employed by a third-party company - I don't remember the details). The passenger asked for a manager, and the person replied that he was a manager. The passenger then asked for whomever was the next person in charge, and the person repeated that he was a manager. The passenger then asked, "So, you are in charge of this whole airport?" which forced the person to admit that they did indeed have a boss that could be summoned.