You seem to have the problem calling it tissue. The two papers Bob linked to that I looked at use the words 'soft tissue.' I suppose the rest do too. I think your suggestion for tissue A & B is good, but you'll need to convince the scientific world.So we're wandering off into semantics. But this is what it means in biology:
If you don't use words as they are used by others, you'll always have miscommunications problems.
Let's differentiate between "tissue A" (the definition above) and "tissue B" (any sort of organic material).
Then we can move on. Clearly, the fossils have "tissue B", under those definitions.