The problem is with SN56.11, not SN56.1. The issue is that, while everyone knows what is meant, there are some statements in SN56.11 that don’t say what was meant. Each of these statements includes a form of the word ariyasacca that doesn’t fit in very well.
IN SN56.1, which you quote above, the language does not “defy grammar” (see an earlier remark in this thread by Bhante @sujato ). The problem only occurs when the word ariyasaccaṁ is connected to a ti clause as in SN56.11. In SN56.1, the ti clauses are clearly understood to be true. They are not explicitly called noble truths as they are in SN56.11. The issue is that “noble truth”, ariyasaccaṁ, in SN56.11 is poorly related to the ti clause. This is what defies grammar.
Additionally, SN56.1 uses the same verb, pajānāti, for each true statement and always uses the 3rd. person singular form. SN56.11, on the other hand, uses different verbs and different verb forms: both the future passive participle (for what ought to be done about each truth) and the past participle (for what ultimately is done about each truth). This creates the semantic problem mentioned above. The problem is most evident in the second truth, where the text appears to say that the second truth should be given up and has been given up. The noble ones, however, do not give up the truth; instead, they give up the cause of dukkha (dukkhasamudaya), which is mentioned in the statement of the truth. The word dukkhasamudaya performs two functions: first, as part of the name of truth" and second as a part of what should be done about that truth (i.e., that dukkhasamudaya should be and later is given up).
It seems that there are two solutions to the problem. Either the word ariyasacca was not present in some of the original statements and, in some cases, the original demonstrative pronouns were different. Or the word was present and the original differed in some way from the unknowable original. (The possibility that the original had the same issue, is, of course, not a solution to the problem.)
It should be noted that Ṭhānissaro Bhikkhu attempts to explain this issue by the analogy between the regional dialects of what is now Italy before the time of Dante [This text, Note 1]. The situation is analogous, however, Ṭhānissaro’s conclusion is a non-sequitur. When one must conclude Q from a true statement P, one is obliged to show that there is something implied by the statement P that combined with known truths implies Q. This obligation Thanissaro fails to discharge. Therefore his argument fails. (This is nothing against Ṭhānissaro. No one reasons perfectly all the time. He may have been mislead because his hypothesis, “Italian was a group of irregular oral dialects until Dante fashioned it into a regular language for the sake of his poetry” is not quite right. Each dialect would have had its own, perhaps unstated, grammar but there was no official standard of what correct Italian was. The dialects were only irregular in hindsight and likely only from an upper-class point of view.)