Yes. "Mint," "Debian," "Kali," etc., don't mean "stop paying attention."
You're right that it's bad to robo-close questions based on the presence of specific keyword or tags, and that this is something that sometimes happens on our site, that it happened in this particular case, and that it needs to stop happening. The question formerly titled Bring Back old GRUB menu? is clearly about Ubuntu, and this was discernible even before it was improved by editing. The original question even said:
Earlier I have GNU GRUB Version 2.02 by Ubuntu.
I want Ubuntu 14.04 at the first position, Linuxmint, and Windows after that.
It doesn't get much clearer than that. This is an on-topic question.
Another recent example, which was also on-topic and also happened to be a duplicate, was originally titled extract a specific program or script from iso, had always been clearly about extracting a file from a Kali ISO image or a device to which such an image had been written, and not about running Kali Linux. But it was still closed as off-topic for not being about Ubuntu. (We reopened it.)
I think the important question to ask when deciding if a question is on-topic is "Is this about Ubuntu?" but unfortunately people often ask themselves "Is this (also) about something that isn't Ubuntu?" instead. That's the wrong question to ask. As I said in Are half-Minty questions allowed?:
A question needs to be about Ubuntu to be on-topic. Whether or not it is also about Mint doesn't really matter.
Note that this should not be interpreted as arguing for a different way to not pay attention. Just as the presence of certain keywords or tags doesn't ensure a question will be off-topic, the word "Ubuntu" is neither necessary nor sufficient to make a question on-topic. In general, noticing specific words is no substitute for figuring out what is actually being said. Because this is about questions that are about Ubuntu but also relate to other topics, the "Respecting your own community" section of Respect the community – your own, and others’ is also relevant.
I agree with much of what Kaz Wolfe has said but I don't agree that we should usually edit "Mint" out of on-topic questions that mention it. It's potentially useful information to know that a problem happened on another installation too, whether or not it is Ubuntu. Furthermore, Mint is similar to Ubuntu in some ways and different in others, and those are both reasons that knowing something affected Mint too will sometimes confer useful information, allowing us to rule out some possible causes of a problem.
How do I close thee, let me count the ways...
I do disagree with part of what you are saying, though, at least as I understand it and as I expect other readers will understand it.
When a close reason is correct, and you have undertaken the necessary care to satisfy yourself that it is correct, you are under no obligation to go looking for another one before voting to close. That is, if an off-topic question could also be reasonably considered a duplicate, you can feel free to close it as a duplicate even though it's off-topic, but you are also free to close it as off-topic even though it's a duplicate, and there is nothing wrong with doing so.
We have no policy about the preferred order of close reasons, nor do we even appear to have any informal agreement about non-binding best practices in this area, nor do I think we really need one. I do actually believe it's better--though by no means necessary--to prefer closing questions as duplicates when multiple close reasons apply. But even that is far from an established consensus. If anything, my opinion on this is the one that is somewhat less popular. See this old conversation, my answer (and its comments) to The quality of the duplicates is so bad that I want to cry, and Braiam's answer (and its comments) to How can we encourage 3k+ users to review more Close Votes.
If you need to close them, I strongly recommend searching for a duplicate first, and before you cast your vote, please make sure that the question is a Mint problem first.
I agree with the second part--when someone is asking about a problem with Ubuntu, their question is not off-topic as a consequence of being related to Mint. However, the reason that GRUB question should never have been closed as off-topic is not that it was sufficiently similar to other questions that it could correctly be closed as a duplicate. The reason it was wrong to close as off-topic is that it was not off-topic, regardless of its similarity or lack thereof to other content on the site.
The Minority Report
When a question is on-topic and a duplicate, and it gets wrong off-topic close votes but also correct duplicate close votes, a bug in the Stack Exchange system frequently exacerbates the problem. As pomsky mentioned and Rinzwind explained, a question with three (or four) off-topic close votes and two (or one) close votes for any other reason will be shown as having been closed as off-topic and the people who voted to close it for the other reason will be falsely shown as having agreed with the off-topic closure. I really hope this behavior of the system gets changed.
If the question is later reopened and people want to close it for the right reason instead, the people who voted for that reason before can't do so again, because when you cast a close vote that is actioned--that is, the question is closed before your vote ages away--the system does not allow you to vote to close that question a second time unless you are a moderator. (That restriction is itself reasonable and generally good and I don't suggest lifting it.) Thus the system makes it very easy to close questions for totally wrong reasons that set a terrible example for us all to follow, then makes it hard to correct the problem.