The punchline:
- It's Dative because Genitive is not clear.
The reasoning:
First of, there is real grammatical reason why it would be Dative.
It does, however, feel right and maybe even better than the cumbersome double genitive-s.
One reason might be that a double genitive is in fact not clear. It could part of a list or, if we don't see the punctuation, it could express possession.
Er steht an der Spitze der Telekom, eines Fussballvereins und eines Buchclubs.
Er steht an der Spitze eines Gremiums eines Vereins zur Verbesserung der Hundeschönheit.
So... not using Genitive makes it clear that we're looking at an apposition. But why Dative and not Nominative?
That might indeed have something to do with "von dem"-idea that @Vogel612 mentioned.
Let's say the sentence end after "gremium"
... an der Spitze eines neuen Gremiums.
If I wanted to know more about this I would probably ask.
Von welchem Gremium?
and not
Welchen Gremiums?
which it would take me a good 2 minutes to think of and construct.