As it turns out, there is an emerging mode of inquiry within the academy that has been described as Buddhist critical-constructive reflection. This is a mode of inquiry that is carried out by religiously committed Buddhists who, adopting the critical, historical and philosophical methods of the academy, aim to explicate the truth of Buddhist doctrine and practice in an open and public manner.
Buddhist critical-constructive critics are academics who are also Buddhist practitioners. They do not simply aim to study Buddhism in a detached manner but are also committed to making Buddhist doctrine and practice relevant to contemporary audiences and to using Buddhist resources to address modern issues.
José Ignacio Cabezón (a Mahayanist) has described this mode of inquiry as:
‘a form of normative discourse that situates itself explicitly and self-consciously within the Buddhist tradition, and that, abiding by accepted scholarly norms, critically plumbs the tradition with a view to making relevant in a public and open fashion the meaning and truth of Buddhist doctrine and practice.’
There is also a recent article by John Makransky in the Journal of Global Buddhism that explicates the idea of Buddhist critical-constructive reflection. The article touches on the issues raised by Ajahn Sujato. See http://www.globalbuddhism.org/9/Makransky08.pdf
To respond to your OP.
Yes, I think it is very important to exercise a kind of historical reflexivity when engaging with Buddhism. All those traditions that Ajahn Sujato mentions have fashioned various ahistorical explanations to establish a kind of 'direct' lineage to the Buddha. But this is something that modern Buddhists do too. We modern Buddhists often slip into a kind of ahistoricism ourselves when we fail to recognise the historically and culturally specific methods of modern inquiry, and claim that we have discovered the 'right' way for engaging with the Dhamma--as if we have a kind of unmediated, 'direct' access to the teachings of the Buddha. This ahistoricism is a bad habit that has occurred throughout the history of Buddhism and that still occurs today.
As I see it, these 'myths' may not be rooted in historical truth, but they are nevertheless products of history. They emerge out of the very real historical efforts of people in different cultures and time who have attempted to make the Dhamma relevant to their circumstances.
From our contemporary perspective and with our modern modes of historically-sensitive inquiry, we can learn much about our own efforts to translate Buddhism to contemporary circumstances by attending to these 'myths' skillfully. Learning about how other people and cultures have attempted to negotiate the Dhamma in different contexts can help us better negotiate the Dhamma in our current contexts.
'Myths' are not inherently bad. 'Myths' do not need to be 'true' for them to work. Think of the many stories and movies that we have heard/read/seen that have inspired us.... how many of them are 'factual'? Do they need to be 'factual' to be inspiring, to open up the space for us to seek 'truth'?
The article by John Makransky is well worth a read.
EDIT: While I do not think that there is anything wrong with 'myth', I just want to add that I agree with Ajahn Sujato that it is problematic when they are used to reinforce religious authoritarianism.