Hi again,
“Adhering to strictly Buddhist teachings” implies having right view. The unlearned ordinary people in this sutta all have wrong view.
The uniquely Buddhist view is not just that the aggregates are not self; it’s also that there also is no self outside of the aggregates. (sabbe dhamma anatta = all phenomena are without a self) The part about “outside the aggregates” is what the eternalists and annihilationists are missing in this specific sutta, hence despite what you’re saying, they aren’t adhering to strict Buddhist teachings. They have wrong views specifically said to come from ignorance.
As I implied, it’s not about specific sects, it is about views. Both Buddhists and non-Buddhists can have wrong views.
It is the exact same quote, so the view he praises elsewhere is in essence still the same. He praises it as “the best of outsiders”, which means it is still a wrong view. But as far as wrong views go, it’s the best, because, as he says, it is closest to cessation.
How can something that is not real cease to exist?
It seems you have difficulty separating the annihilationist position from the Buddha’s as I understand it. I’ll try to explain once more. The annihilationist imagines a self, or “I”, or “me”, whether inside or outside of the aggregates. Such a thing doesn’t really exist, but they think that it does. As annihilationists they think it is destroyed at death. The Buddha saw reality as it is and realized there is no self or “I” or “me” at all. So it can’t be destroyed at death either.
If you still can’t see the difference, even if just from an intellectual point of view which you may of course disagree with, I’m afraid this discussion isn’t going anywhere. 
The “me” is the problem here. They think there is a “me” who has no self, but in reality there is no “me”. As the standard reflection says: “not me, not mine, not a self”.
It could be read in that way, although I’m not convinced. I think it means “I have no self” (i.e. there is no self for me) Either way, it doesn’t matter, because the “me/my” still is the wrong perception, not the “no self” part.
That’s not what it says, though. It’s ‘natthi me attā’t, not natthi atta.
These are all views of “my” or “self”.
Throughout the entire canon “there is no self” is never said to be a wrong view. The Chinese canon a number of times explicitly says it to be right, and the Pali canon also points at this, most notably in MN22.
a self and what belongs to a self are not actually found
This means a self and what belongs to a self don’t actually exist.