First off, the meta question you linked to doesn't discourage arguing to reopen a question so much as discouraging floods of "Why was this question deleted?"-style questions which show no actual effort to understand why, rather they just demand someone explain it to them (and, in my experience, argue with whoever actually does take the time to explain it).
Questions can be closed and deleted by anyone in the community (who have earned the privilege), but they can also be undeleted and reopened by the same; if you feel that a closure or deletion is unwarranted, meta is an excellent place to present your arguments.
In other words:
- Demanding that a question be reopened because you disagree with the closure = BAD
- Presenting an argument that the site is better off if a question is reopened = GOOD
If you know why a post was closed, and disagree with that reason, feel free to make a sound argument against the closure; the community may be swayed to agree with you and work to reopen the question. Of course, the community may also not agree with you and decide to keep it closed (communities can be funny like that).
As for the actual question you asked, regarding what moderators do and do not see:
First, you need to recognize that as a community-moderated site, all users are considered moderators, with the power they wield directly correlated to their reputation. Diamond moderators are a special case with extra powers, but they are generally needed to handle exceptional circumstances when the community itself is unable to.
Similarly, the Stack Exchange framework decides who sees what based on who is expected to be able to handle it. For example, casting a reopen vote (or editing a closed question) will automatically push a post into the review queue; this is available to all users on the site who have the ability to reopen posts. However, acting on any given item in the queue (as compared to leaving it for others in the community who are more knowledgeable about the topic) is entirely a personal (and subjective) decision
If high-reputation users who actually have the power (and expertise) to curate the site but can't be bothered to actually review the review queue and use that power, that's a community problem. Sure, diamond moderators are part of the community like any other (and can also review the review queue), but whether they choose to cast their own (binding) vote on anything is again a personal (and subjective) decision.
Flagging a post for moderator attention will (obviously) bring it directly to the attention of the diamond moderators. However, this normally shouldn't be used for issues that the community is expected to handle themselves (e.g. closing/reopening, deleting); diamond votes are powerful and binding, and expecting them to do most (or all) basic curation tasks is akin to calling in an air-strike to handle a mosquito. Diamond moderators are human exception handlers; they are expected to handle situations that the community cannot handle.
If there's a clear case of community-fail (i.e. the community should be handling something itself but for whatever reason isn't) then yes, involving diamond moderators is perfectly reasonable: Presenting such a case is a perfect use for meta. And just like the community, diamond moderators can be swayed to agree with a well-presented argument. But again, they can also not.
But if it is (or at least appears to be) a situation that the community should be able to handle and no attempt was made to actually engage the community to handle it first, or to explain why this should be treated as an exceptional circumstance, don't be surprised if such a flag is rejected.