I answered a question today, which was a mere experience, related to the problem, but not exactly a specific answer...
Is that really allowed, or does each post need to have a proper, specific answer to the specific problem?
Link: My Answer
As long as they are detailed and don't only offer a 'mere' suggestion but also explain why the suggestion worked in your case or might work in theirs.
We have had discussions in the past about the back it up rule and we have also had (now) site moderators reaffirm your suspicions.
Written in Against the evidence or experience requirement within @Catija's answer it states:
We must require answers that address the specific question asked directly and these answers must be supported with either personal experience or a reference. Answers that do not meet this requirement should be either downvoted, commented on for improvement, or outright deleted. Once we have moderators, they can use post notices to request improvement.
It does and it doesn't. You're offering your own personal insight which is great and telling the OP he should care less. Which can be a good solution in some ways, but with just a suggestion to do that is quite vague to some people, as it can be interpreted in different ways.
Some may take it to the extreme and literally not care at all, but in this case, the OP can't help correcting people so that extreme won't be an option here, so a middle ground might work. To improve your answer to make it a good quality answer, I personally would add a couple of times caring less specifically in a conversation helped you avoid correcting a person in the past, what did you do that helped you, that might help the OP? Currently, your answer says what to do and how people perceive it, just not about correcting itself.
I recently asked the question Should I always ask a dog owner before I pet their dog?
The most upvoted answer is brilliant, it not only answers the question directly, it also offers in great detail as to why you should always ask, why they would want someone to ask and why their dog is not in a position to just be petted without them being notified. This should be used as a reference for future experienced based answers, it's a very high-quality answer and has been confirmed by the community with the sheer amount of votes it has.
Basically, if you directly answer the question and explain in detail why your experiences help answer said question. You'll have a good quality answer.
I try to offer my own personal experiences and then see if there are any references on the internet that also back up what I'm saying and add them in. I'm not saying you always will be able to, but it's that little bit of extra information for future readers or the OP to take away.
In this case what you call 'mere experience' is also a very good answer to OP's question, because you have been in the same situation as OP and you have been able to clearly communicate how your problem developed, when you became aware of it, and what steps you took to put it right. Without telling OP "you should do thus or thus to solve your problem" you have simply said "I had the same problem as you have, and this is what I did to successfully solve that problem." That method of writing an answer is perfectly acceptable on IPS.SE!