must vs have to: British usage and academic rules

I am teaching 'have to' vs 'must' (British English usage) and, according to the book, the difference is as follows:

must: it's necessary to do it (because the speaker says so)

have to: it's necessary to do it (because it's a rule or law)

The students had no difficulty with these ideas and applied them appropriately, both orally and in the initial exercises. But then we came across the following sentences:

1. Passengers must / should remain in their seats while the plane is landing.




2. Students must / may be silent during the written exam.

Both sentences present rules, not situations where the 'speaker says so', so why is the correct modal 'must' and not 'have to'?

I can only assume that the rules presented are incomplete (it happens the same when teaching Present Continuous, which is first taught without mentioning its future arrangement function). But I cannot find a single school book where any other rule, or even exceptions, are mentioned.

I have also searched EL&U and I did come across two related questions:

1. "I have to" vs. "I must"

It's mentioned that 'have to' usually implies an obligation imposed by somebody other than the speaker and that 'must' is usually a personal obligation. This follows the line of the rule in my book and, again, fails to explain the sentences above.

2. What's the difference between "I must help her" and " I have to help her"

It's mentioned that, although 'must' is supposedly for personal obligations it can be used for external obligations, and there's even the example "You must show your ID card" which is in line with the two examples from my book.

So I can't help but wonder: why is 'must' preferred in the two sentences above when the rules would have you use 'have to'? And also, when is 'must' preferred over 'have to' to express external obligation?

I'm particularly worried about this because the students became confused and I have no explanations for them.