A paper published in Nature Communications discusses a recent discovery:
“Here, we document a fossil of an Early Cretaceous bird, Confuciusornis sanctus, which has some strikingly well-preserved soft tissues around its ankle joint. Microscopic analyses of these tissues indicate that they include tendons or ligaments, fibrocartilages and articular cartilages, with microstructure evident at the cellular level.”
“Further chemical analyses reveal that even some of the original molecular residues of these soft tissues may remain, such as fragments of amino acids from collagen, particularly in the fibrocartilage. This concurs with accruing evidence that some biomolecules may survive, under exceptional circumstances, over many millions of years.”
A more logical explanation would be that the fossils are not that old. Soft tissue might last a few thousand years in exceptional circumstances, but not for many millions of years.
Jiang, Baoyu et al. 2017. Cellular preservation of musculoskeletal specializations in the Cretaceous bird Confuciusornis. Nature Communications 8:14779.