I think it was the other way - fungus from the trunk attached to the tillandsia leaves.

Apparently ants like some Tillandsias, particularly those with bulbous bases (like seleriana), where the ants can set up home away from home. They may have carried some fungus along as they explored the bergeri, and unintentionally planted some on the tips -- maybe to keep the bergeri stuck there so they (the ants) could use it like a bridge to someplace else. Just a thought.

It was very solid. Like rooted solid. I saw nothing but that rotted trunk did have fungi. I had to tug. Yet,the leaves are perfect.

Must be some kind of secondary..fungi- plant association?

The fungi might be only from the rotted trunk then and maybe crept onto the Tillandsia, which was ignoring it. If the Tillandsia wasn't over wet, it probably was unharmed (in nature they'd be clinging to trunks that would surely die and rot, too). I suspect that fungi, algae and other "problems" don't have a lot of success on healthy plants, but do good work breaking down dead vegetation and turning it into compost.

The leaves being perfect is good. And if when you tugged the plant off the leaves were damaged a bit, in nature they'd have the same problem (say, an animal or bird giving it a taste test) and the plant would make every effort to recover from the challenge. So since you are taking good care of it, I think you and it are safe.

If you want the plant to cling to something and you would like it to look like wood but without the rot problem, I suggest finding some nice pieces of petrified wood (at a rock store or a gem & mineral show, or even out in the wild). Raw and not varnished in any way. I have some plants (mostly ionantha) that have stuck roots to small rocks and even the sides of glass cups, that kind of thing. Also I've collected fallen wood and have an ionantha that has sunk root into the inside of a piece of long, thin (dried out) bark (cottonwood or elm maybe). I've put other ionanthas near the rooting plant on the same piece of bark; maybe they'll root, too. These I will in the future spray water on, not dunk in water, or that wood will deteriorate faster when wet.