Yes, it's certainly useful to have the subtleties (or not-so-subtleties) of the history pointed out...
Besides, even if one takes a Classical Theravada version to be authoritative, and the other sects as suspect, then, as I understand it, one should neither dismiss teachings from other schools, nor accept without question teachings from post-Canonical Theravada teachers (ancient or modern) but should check everything for consistency against the Tipitika and Canonical Commentaries (as in the OP of this thread...).
Well, it is worth noting that in recent times, the very question of whether Nagarjuna's MMK text is strictly speaking a Mahayana text or not, has been risen.
Traditionally, given that elsewhere a large number of important Mahayana treatises are attributed to Nagarjuna, it was often (almost always) considered that the MMK was also representing such a Mahayana POV. The (previously mentioned) source bias approach of "if it isn't Theravada, it must be Mahayana" was applied, and since there are some points in the MMK which are not in conformity with the Theravada (commentarial / Abhidhamma) position, it was thought - "Yes, it's Mahayana".
But, now that there is an attitude of making a distinction between early Suttas, and the later Theravada Abhidhamma / commentarial tradition, this has been brought into question. Key points include, that the MMK does not directly cite any Mahayana texts, and that no mention of a Bodhisattva path (etc.) is mentioned. Re the former, there is a parallel passage between the MMK and the early Prajnaparamita, but again, this does not necessitate "borrowing" or "citation" of Nagarjuna from that text, as the passage is something that would have been accepted by a number of early schools. Could be a "same source" issue, not one from the other other.
This question of Nagarjuna's MMK being a non-Mahayana text was raised in the West a few decades ago, and people like Gombrich and Vélez de Cea, have written on it. However, again, they only use the Pali suttas as material to investigate this matter. Before these Western scholars made such statements, Yinshun said:
“The Middle Śāstra (中論 Mūlamadhyamaka Kārikā [with commentary]) is a śāstra to elucidate the Āgamas”, and “the Middle Śāstra takes the perspective of the Mahāyāna scholars … and selectively develops the profound meaning of dependent origination in the Āgamas, and firmly establishes the right view of (Mahāyāna) Buddha Dharma on the key-stone of dependent origination, the middle way.”
 [Yinshun “Modern Discussion on the Madhyamaka (中觀今論)” in Collection of Sublime Clouds (妙雲集), p. 18, 24. 1949]
That was written in 1949!
To make things more tricky:
So, getting back to the issue of "should check everything for consistency against the Tipitika (sic) and Canonical Commentaries", one still has to ask the question of - The Tripitaka and commentaries of which school? Now here, it is going to be Theravada, but if one wishes to open things up to a broader perspective, and in my view, this is really necessary, then one is going to have to go further than that. Given Walser's comments, the Mahasamghika Tripitaka would be the place to start, but we don't have this. Can we really ever do justice to Nagarjuna, then? Or, are we just going to measure him by the standards of some other school?