Yes, there are some misunderstandings about the Hennessy insulation options. But then Hennessy actually has a few different options, so it can be confusing.

The radiant bubble pad is the only item that might be used inside your hammock. It's actually meant to go in between the layers of a double-layered hammock, but if you wanted to use it in a single-layer hammock, you could bring it inside and lay on top it as it's meant to be non-compressible.

Then they have compressible, foam pads than hang under the hammock (part of the Super Shelter system). They are functionally similar to an under-quilt, but don't necessarily pack as small, and are not as warm as some quilts.

And they have the undercover, the other part of the Supershelter. That's another, thin layer than hangs under the hammock, under the foam pad, that acts as a windbreak. The undercover on it's own, just as a windbreak, provides a little protection. I leave mine on all the time except when it's very warm, in which case I have to remove it to stay comfortable. Also you can use the undercover to hold other items: a space blanket, an actual quilt, spare clothes, etc. Anything that provides extra insulation.

I have found that the Super-Shelter combined with a space blanket can keep me comfortable down into the upper 30s (Fahrenheit). Any colder and I'll want some additional insulation down there.

The other piece of the Hennessy insulation system is the over cover. The overcover goes over the bugnet, outside the hammock, to provide an additional windbreak. It's not a replacement for a quilt or sleeping bag. It just keeps airflow from leaching heat out of the hammock.

So the only piece of Hennessy insulation that might be used inside the hammock is the bubble pad. And the only other insulation you would want inside is a quilt or sleeping bag.

I find that the SuperShelter, plus a space blanket, and a temperature-appropriate sleeping bag meets most of my needs. Then if it's too cold, I add the the overcover and maybe some additional insulation underneath.