I just requested information about a chalet to purchase but the real estate agency said they could only sell to a Swiss citizen or C permit holder. I am dual (Italian/US) with a B permit. Have I missed something about my rights as an EU citizen? I understood I could buy property (even a holiday home).

No, you are not wrong.

https://www.ch.ch/en/real-estate-foreign-national/

However, there are some odd rules about holiday/second homes so worth checking with the commune/gemeinde to see if there are any restrictions.

What nationality did you use for your enquiry?