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

Page 576 of Collins English Usage reads

When you are talking about your own intentions, you use will or be going to. When you are talking about someone else's intentions, you use be going to.

I'll ring you tonight.

They're going to have a party.

Why can't will be used for somebody else's?

Solution 1:

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.