I remember asking a similar question regarding a planet's atmosphere a while back, and one of the things I'd read about argon (and other similar noble gasses) was, as you stated above, that it's heavier than Earth air and tends to sink. That said, in a human respiratory system, it would have a tendency to collect in the lungs since our diaphragm is used to expelling lighter gasses.
Even if the rest of the atmosphere isn't poisonous, breathing an atmosphere that is comprised mostly of argon (like our own atmosphere is comprised mostly of nitrogen) would eventually cause asphyxiation as more and more argon collects in the air sacs, displacing the lighter vital gasses we need to survive. Don't quote me, I'm not a scientist, but that's the conclusion I drew from what I found.