Miyagawa and Arikawa 2007: 654 states:

***
If the universal occurs in subject position,it is most naturally interpreted under neutral intonation as being outside the scope of negation; most speakers find it difficult,if not impossible,to interpret it inside the scope of negation (Kato 1988).

(20) Zenin-ga tesuto-o uke-na-katta.FN3(not provided here, HH)
all-NOM test-ACC take-NEG-PAST
‘All did not take the test.’
‘*not > all’,‘all > not’

Crucially, as pointed out in Miyagawa 2001, if the object scrambles across the subject zenin, the partial negation reading becomes easier to obtain.

(21) Tesuto-o_i zenin-ga t_i uke-na-katta.
test-ACC_i all-NOM t_i take-NEG-PAST
‘That test,all didn’t take.’
‘not > all’,‘all > not’

(20) and (21) are diagrammed as in (22) and (23),respectively.^FN4

FN4: An anonymous reviewer asks precisely what the difference is in entailment between (20) and (21). For example, it is distinctly odd to follow (20) with Hanako-wa uketa ‘Hanako took it’ because (20) entails that no one took the test, but it is completely natural to follow (21) with this statement since (21) entails only that some people failed to take the test.
***End of Quotation***

It should be more than "distinctly odd." It should be a contradiction to follow (i-a) with (i-b), provided that it is clearly understood that Hanako is among the people under discussion.

(i)　a.　No one came.
　　b.　Hanako came.

For example, the sequence in (ii) and (iii) are felt to be clearly contradictory, provided that it is clearly understood that Mary is one of the examinees. (ii) and (iii) differ from each other only with respect to the order of the subject and the (ni-marked) object in the first sentence.

(ii)　Zyukoosya-ga hito-ri-mo ankeeto-ni kotaenakatta.
　examinee-NOM one-CL-also questionnaire-DAT did:not:answer
　'None of the examinees answered the questionnaire.'
　Mary-wa tyanto kotaeta kedo.
　Mary-TOP neatly answered but
　'Mary answered (it) neatly, though.'

(iii)　Ankeeto-ni zyukoosya-ga hito-ri-mo kotaenakatta.
　questionnaire-DAT examinee-NOM one-CL-also did:not:answer
　'None of the examinees answered the questionnaire.'
　Mary-wa tyanto kotaeta kedo.
　Mary-TOP neatly answered but
　'Mary answered (it) neatly, though.'

Furthermore, according to M&A's claim, (iv) and (v) are as contradictory as (ii) and (iii).

(iv)　Zen'in-ga ankeeto-ni kotaenakatta.
　all-NOM questionnaire-DAT did:not:answer
'All did not answer the questionnaire.'
　Mary-wa tyanto kotaeta kedo.
Mary-TOP neatly answered but
　'Mary answered (it) neatly, though.'

(v)　Zen'in-ga a-no bakarasii ankeeto-o musisinakatta.
　all-NOM that-GEN stupid questionnaire-ACC did:not:ignore
　'All did not ignore that stupid questionnaire.'
　Mary-wa musisita kedo.
　Mary-TOP ignored but
　'Mary ignored (it), though.'

According to M&A, (iv) and (v) should contrast sharply with (vi) and (vii).

(vi)　Ankeeto-ni zen'in-ga kotaenakatta.
　questionnaire-DAT all-NOM did:not:answer
　'All did not answer the questionnaire.'
　Mary-wa tyanto kotaeta kedo.
Mary-TOP neatly answered but
　'Mary answered (it) neatly, though.'

(vii)　A-no bakarasii ankeeto-o zen'in-ga musisinakatta.
　that-GEN stupid questionnaire-ACC all-NOM did:not:ignore
　'All did not ignore that stupid questionnaire.'
　Mary-wa musisita kedo.
　Mary-TOP ignored but
'Mary ignored (it), though.'

　I conducted an on-line experiment a few years ago (February, 2007) on this. Included in the experiments were examples like (ii)-(vii). Examples like (ii) and (iii) were judged clearly unacceptable by most informants, as expected. With 26 informants on the 0-100 scale (0=completely unacceptable and 100=fully acceptable), the average scores for (ii) and (iii) were 0.96 and 1.92, respectively.

Now, Examples like (iv) and (v) should be as unacceptable as (ii) and (iii), but the judgments by the same informants on those were 48.18 and 50.96. Examples like (vi) and (vii) are judged somewhat more acceptable than those like (ii) and (iii), with (vi) getting 72.12 and (vii) getting 58.65. But, the improvement here is not significant because examples like (iv) and (v) are judged fairly acceptable, to begin with. (Notice also that there is also improvement in (iii) over (ii).)

If you want to check some of the relevant examples with native speakers of Japanese, you can show the following examples and ask them how they find these examples. (viii) is a "control" example; it is a version of (v) that is contradictory.

(ii) 受講者が一人もアンケートに答えなかった。　メリーはちゃんと答えたけど。(Score: 0.96)
(iii) アンケートに受講者が一人も答えなかった。　メリーはちゃんと答えたけど。(Score: 1.92)
(iv) 全員がアンケートに答えなかった。　メリーはちゃんと答えたけど。(Score: 48.18)
(v) 全員があの馬鹿らしいアンケートを無視しなかった。　メリーは無視したけど。(Score: 50.96)
(vi) アンケートに全員が答えなかった。メリーはちゃんと答えたけど。(Score: 72.12)
(vii) あの馬鹿らしいアンケートを全員が無視しなかった。　メリーは無視したけど。(Score: 58.65)

(viii) 受講者が一人もあの馬鹿らしいアンケートを無視しなかった。　メリーは無視したけど。(Score: 6.73)

In line with the methodological proposal summarized in Methodology [42404], there is NO POINT to continuing to use the alleged generalization or the proposed "theoretical" account of it IF one is interested in discovering something about the properties of the Computational System of the language faculty.

As I indicated in Generalizations [42432], the alleged generalization concerning Negation and a scope-bearing element is not a special case. The fact that it has continued to be used for all these years and is still being used now is beyond my comprehension. I think it is in part a reflection of the fact, I think it is a fact, that people just do not think it is possible to approach the language faculty by rigorously applying the hypothetico-deductive method. (And hence they think that they can only talk about" it, without seriously pursuing rigorous testability. "Judgments are always murky and we must live with it..." Please see the methodological proposal summarized in Methodology [42404] for how we can aspire to do much better than that. If you are interested in learning more about it, please email me.