What is the humidity level in the basement? I suspect it is high and you are seeing condensation on the cold duct work.

You may need to install a dehumdifier in the basement. I would try this before adding insulation.

I had a similar problem two years ago with a new basement Carrier installation. The instant fix was to insulate - it took about an hour and was 100% effective - and done at no charge.

I had added a return in my basement concurrent with the install and in a week or so the humidity level in my basement had dropped nearly 10%.

The addition of a basement dehumidifier will have a measureable impact on your monthly electric bill.

That is sure odd, I would try insulating too. You could also use a dehumidifier. We use one and it sucks so much condensation and water out of the air. Our basement used to be a bit stinky, not anymore. Let us know how you make out if you insulate the area.