Did you inform the landlady of the flood? If so, you did what you should have done, by informing the landlady of the flood and taking responsibility.
The landlady then should have taken it upon herself to get the place inspected, dried out, etc. She could have charged you for the inspection, and the drying out process. By not doing this, regardless of what the other tenant said, she was neglectful in her duty to minimize damages.
Even if you didn't inform the landlord, it's my opinion that the other tenant was responsible to tell the landlord about the flood. It's very likely that the lease includes a clause that tenants are to let the landlord know about issues that may cause damage. A flood definitely needed to be reported, as further damage could obviously occur if not addressed right away.
Sounds like the other tenant didn't do their duty in reporting the flood in a timely manner.
So, I see the landlady as being negligent, and possibly the other tenant being negligent, as well, as far as doing their duty to minimize the damages.
Anyway, I'd fight this based on the above. You did your duty, LL and tenant didn't do theirs. It was their negligence that caused the damage to become severe.
In Hawaii, the law says people who are negligent share the blame. The simple explanation is that for the landlord to recover damages from you, you would have to be more than 50% at fault for the damage that occurred in the other apartment. I don't think that's the case.
I'd try a letter to the landlady like this. If this doesn't work, you should contact legal aid or your tenants union, etc.
Dear LL:
As you know there was a flood in my apartment on ___________________(date). The water from this flood entered the apartment below me, #________________.
On _____________(date), I discussed whether or not there was any damage to apartment #____________ with the tenants below me, and whether or not there was anything further I should do to minimize damages, and they informed me that they were able to clean up the water, and that there was no damage, and that nothing further was required of me to minimize further damages.
On ________________(date), I informed you of the flood, and the fact that water seeped into the apartment below me.
On __________(date) I received a letter from you, a month after the flood, stating that there was damage in apt #_________________ due to the flood , which occurred subsequent to my informing both you and the tenants below me of the flood, and my conversation with the tenants in apt #__________, in which I attempted to mitigate damages by asking if there was anything further needed regarding damage.
You, as the landlord, had a duty to mitigate any damages by inspecting apt #________ to be sure there would be no further damage due to the flood. The tenants in #_____________ had a duty to inform you of the flood, regardless of their opinion of whether or not they were able to clean up the water completely, as any flood of this type is likely to cause further damage.
The tenants in apt #_____________ were negligent in reporting the flood, which resulted in further unnecessary damage.
You, as the landlord, were negligent in insisting on a complete inspection and having any required work done that would have mitigated damages.
As Hawaii has a modified comparative negligence law. First, the injured party may recover only if he or she is less than 50 percent at fault. Second, if the injured party was also negligent, the original negligent party is only liable for the percentage of damages he or she caused.
As you know, I have repaired all damage to my apartment, at my own cost and/or through my renter's insurance policy.
The damage resulting from neglect by you and/or the tenants in apartment #__________, to immediately deal with any potential flood damage, is not my responsibility under Hawaii law.
Sincerely,
You
If you didn't inform the landlord of the flood, just leave that part out. The tenant below you should have done so. Regardless of whether or not they believed they cleaned up the mess.
Here is a link that simply explains Hawaii negligence law, in case you need to refer to it:
http://www.yourpersonalinjurylegalguide.com/hawaii.htm
Even though it's about personal injury, the law would also apply to other types of negligence. Scroll down to the section titled "Negligence."
Good luck!