> But
https://languagelog.ldc.upenn.edu/nll/?p=2922 "The passive in English" says:
>> The relevance of participles is that a passive clause always has its verb in a participial form.
> So, what are you saying they do think it was meant to apply to, if every passive clause always includes a participle? I'm confused.
OK, you're confused.
In the general case, an English verb has five forms†: "plain form" [go], "preterite form" [went], "present third-person singular form" [goes], "-ing form" [going], and "-en form" [gone].
The last two of those are participial forms.
It is true that a passive clause always has its verb in a participial form. We can be even more specific than that: the verb is always in -en form. This is true without exception because passive markers occur last in the sequence of auxiliary verbs that might modify a primary verb, and therefore always directly control the form of the primary verb.
It is not true that a passive clause always includes a participle, except in the sense of the name we give to the form of the verb. -ing and -en are "participial forms" because the verb takes one of those forms when it is a participle. But it can also take them for other reasons.
> the passive-clause examples given in Pullum's blog post I linked above include "Each graduate student is given a laptop," which sounds structurally identical to your example
Sure. If you wanted to put the present passive third-person plural form of make in that sentence, that form† would be are made. The sentence would have all the same words in the same order.
But that would make no semantic sense. For a point to be "already made", as opposed to having "already" been "made", you need to interpret made as an adjective, describing the state in which the point currently exists. The temporal structure of "each graduate student is given a laptop" differs from that of "in addition to the points that are already made" in a way that allows the present noncontinuous form of the verb. I don't think that works for "the points that are already made"; if I try to interpret that as a passive verb in the present tense, I get a strong sense that the sentence is malformed.
† You might notice that these two uses of the word form conflict with each other. The fact that form is used in both of these ways is why I'm annoyed at your comment conflating "participle" with "participial form". "Participle" is appropriate when you're talking about inflecting a verb according to how you want to use it in a sentence; it is a concern with the language's grammar. "Participial form" is appropriate when you're talking about the actual tokens that can appear in a sentence, with no regard to what they might mean or how they might be used; it is a concern with what you might think of as the language's "anatomy".