"Will" not used for somebody else's intentions/plans

This seems to be an example of poorly supported prescriptivist grammar.

From The Cambridge Grammar of the English Language p192-194, a modern descriptivist grammar,

Dynamic Modality

Under this heading we consider those uses of will where dispositions or properties of the subject-referent are involved.

(a) Volition

[38] i Jill won’t sign the form.

ii They have found someone [who will stand in for you while you’re away].

iii I will be back before six.

Example [i] implies unwillingness or refusal on Jill’s part; in[ii] will might be glossed as “is prepared/willing to”; and in [iii] the auxiliary conveys the idea of intention.

...

[39] i I WILL solve this problem. [strongly stressed modal]

ii Will you lend me your pen? [closed interrogative]

iii I’ll wash if [you will dry]. [conditional protasis]

A strongly stressed will, especially with a 1st person subject, tends to convey determination. A closed interrogative, especially with a 2nd person subject, characteristically questions willingness and indirectly conveys a request (Ch. 10, §9.6.1). Futurity will rarely occurs in a conditional protasis, as noted above, but volitional will is quite unexceptionable, as in [iii], where your willingness is clearly part of the proposition that is conditionally entertained.

Extension to inanimates

Volition implies a human or animate agent, but something akin to a metaphorical extension of volitional will is found with inanimates when it is a matter of satisfying human wants,as in The lawnmower won’t start (someone is trying to start it)or >The books won’t fit on one shelf. These again appear freely in conditionals: Give me a call if the engine won’t start.

The examples given in [38-39] (excepting the first person ones) can all be interpreted as expressing the intentions of other people.