Conclusion (Edit 2): The HE staff replied:
We understand your concern. It's a known issue and we are already in the process of fixing it. We will get back to you once it's fixed.
I have massive respect for these guys, I don't think I even waited a full day for the response. Anyway, mystery solved.
Edit: Since it seems there is no consensus on why the following is present on the site, I've sent the team an email and will update this post with information when they reply.
On a contest page, it seems that even post-contest, if there are incorrect test cases but at least one is correct, the problem is marked solved like so:
It's the same on the problem's My Submissions page.
However, if you look at my submission, I have nine incorrect test cases.
Is this a bug or a feature, speaking objectively?
If it's a bug, I'll report it, and if it's a feature I'd like to know its purpose as it seems misleading to think you may have solved a problem when there could be incorrect test cases.