The difference is what follows in the second clause. To quote from the 大辞林 entry for って
The important thing is that the clause that follows is contrastive to the clause that ends with って.
In the first example, the first clause tells us that Marie Antoinette used to sit on the chair.
これがかの有名なマリー・アントワネットが座った椅子だ This is the chair that the famous Marie Antoinette sat on.
これがかの有名なマリー・アントワネットが座った椅子だった This was the chair that the famous Marie Antoinette sat on. (maybe it's only the remnants of the chair now)
And the second clause according then contrasts the fact that she used to sit on that chair with the fact that now (今) she cannot possible be sitting there. The fact that the chair could not be fully functioning doesn't matter
But in the second example, the implication in the second clause is that even a cute dog could bite you. However, depending on だ and だった, the implication about the current state of the dog is different.
榊さんの飼っている犬がかわいい犬だ The dog that Sakaki-san owns is a cute dog.
榊さんの飼っている犬がかわいい犬だった The dog that Sakaki owns was a cute dog (but isn't anymore)
If we use だった, the implication is that the dog that Sakaki-san owns is already no longer cute (maybe he was a cute puppey or something), so then it wouldn't be unexpected at all for a mean dog to bite you. Thus the second clause isn't contrastive compared to the first clause.