Just because the Federation doesn't use physical money, that's not a logical reason to assume the Federation doesn't have an economy. Any group of people larger than a band (anthropologically speaking) has to have some kind of economy, even if it's just bartering.
We saw numerous examples in TNG of Federation citizens interacting with non-Federation citizens for the purpose of commercial transactions, whether it's with the Ferengi or that friggin' bolt of cloth Beverly charged to her account on the Enterprise in "Encounter at Farpoint."
So there's nothing wrong with Offenhouse holding that job or title.
What is wrong is the incredible hypocrisy of Picard, et. al in denying that the Federation uses money. Of course they use money. They just don't use hard, physical currency.
Unless, of course, they're gambling at Quark's, on Deep Space Nine. I wonder where Jadzia kept her stash of gold-pressed latinum - under her pillow, under the mattress, in her boot, or somewhere else?