Earlier quoted context omitted.
Forced air and radiators dry the air equally. Steam radiators sometimes can add humidity to the air it is limited and only when they are initially heating up before the valve closes. What causes dry air in the winter is the act of heating air up. Relative humidity is based on the temperature of the air, so if there is a fixed amount of water in the air, as you heat it the relative humidity goes down. So in the winter…
The way I understand this at the gut, conversational level, is by noticing that hot air can carry more water, therefore it will dry your skin faster, which is what "feels" like the air being dry. Heating doesn't remove water from the air, as you explained. But that's what people assume when they argue that "heating doesn't dry the air" as I've heard in the past. Using relative humidity is a good explanation.
Radiant heat feels somewhat different than warm air, but if radiant heat from the radiators of a steam or water system is significant, would that not make them feel dryer? Our house has water radiators, and I do not notice the radiant heat from them.
I believe Retric's explanation is the correct one, given that human activity tends to increase the absolute humidity of interior air.