Just scanning the correspondences tables at Sutta Central, I get the feel that the known Tibetan parallels to the Nikayas is pretty thin. Maybe more work needs to be done.
Even then, Ajahn Sujato mentioned once that when the "Agama" sutra authorities from the Abhidharmakosa were examined, they did not quite match the Agama sutras that have been preserved in the Chinese. Was Vasubandhu perhaps working with sutras that have evolved further after the Chinese Agamas closed?
It's a loss for the Tibetans that they don't have access to the old texts. Until more Tibetan monastics catch up with the Chinese and Japanese counterparts with solid comparative Buddhism degrees, they are just going to perpetuate the silly Gelug mythologies about the textual traditions a la "Maps of the Profound". But then again, even if armed with a PhD, would a Tibetan monastic dare disavow such a historiography that is entrenched in the tradition of Vows?