As far as I can tell, Buddhayana simply means you're a follower of the Buddha and aren't inclined to lock yourself into the doctrinal positions of the various schools... a non (or multi?) denominational Buddhist. The problem with Buddhayana tends to be the supersessionism inherent within Mahayana and Vajrayana, rendering the Theravada teachings as of lesser importance.
Buddhayana should not be confused with Buddhavacana (word of the Buddha), which is an attempt to use whatever means are at one's disposal, to find out what the Buddha actually taught and what he didn't... and follow only that which he taught! I consider this to be a legitimate approach to the Dhamma, but you need to be honest with yourself and have to agenda to push. Some people often use a Buddhayana style analysis to push their own pet theories.
As traditions/approaches/schools, both of the above are reasonably new and informal in their structure.
Through corruption of the Dhamma comes corruption of the discipline, and from corruption of the discipline comes corruption of the Dhamma. This is the first future danger as yet unarisen that will arise in the future. You should recognize it and make an effort to prevent it. (AN 5.79)
Neither traceable in the Discourses nor verifiable by the Discipline, one must conclude thus: 'Certainly, this is not the Blessed One's utterance; this has been misunderstood by that bhikkhu — or by that community, or by those elders, or by that elder.' In that way, bhikkhus, you should reject it. (DN 16)