No, it has nothing to do with Buddhadhamma. Nor does it have anything to do with Theravada. There has never been an "official" Theravada doctrine that suttas can't be taught to lay people. That is just something that certain people in certain cultures decided to do. If one wants to break with that tradition he could just say "I'm breaking with the tradition of not teaching Theravada scripture to lay people. I will teach Theravada scripture to lay people." Then we could see there are Theravadins who teach scriptures and Theravadins who don't.
By rejecting the word "Theravada" and creating a new word "Buddhayana" one is not simply rejecting certain cultural practices but rather one is rejecting an entire body of doctrinal understanding.
Lord Buddhas teachings and Ajahn Buddhadasa's as well were all connected with Voidness, in truth there is no Theravada, no Mahayana, Vajrayana etc there is only Buddhadhamma, by using the term Buddhayana (i assume) Ajahn Buddhadasa was stating that there is no "Theravada" Buddhism or "Mahayana" Buddhism, there is only Buddhadhamma and so in conventional speak, Buddhayana
Lord Buddha wasnt a Theravadin, a Mahayanist or any other label
What Ajahn Buddhadasa did was get down to the core of Buddhadhamma, that which unifies all the schools and so cant be called "Theravada" or "Mahayana"
In short he focused on what is really important in Buddhism, Dukkha and its quenching, those small handful of leaves