Is it possible to confirm hacking the server logs and present it in court?
Very difficult, almost impossible, and most importantly -
why???
As the owner of the resource you have administrative responsibility for the placed materials - no matter hacked the server or not.
Regarding criminal responsibility if there is something serious, then it is the prosecutors will have to prove that it was you who posted the entry.
Therefore, you do not need to do.
Once again - as the resource owner, you are responsible for the fact that it is placed. Regardless of break-ins and other things. Ie, you are guilty even if you were hacked.
So they claim it to you, and that you will respond. And with the burglar can be dealt with separately - to announce the fact of burglary to the police.
It is in theory.
In practice, plaintiffs would be extremely difficult to prove the fact of placing the material if it is already deleted. Unless of course you will have a competent lawyer. Well, the fact that they tried to resolve this situation with you without the involvement of the court, will play against them.
In General if you just threaten to court trying to shake down, feel free to send away, without a word.
If actually filed a lawsuit - hire a competent lawyer, and then act on its advice.
And nothing else. - earl.Weissnat commented on July 9th 19 at 10:55
Thanks for the advice, probably will have to splurge on a competent lawyer and follow his recommendations) - tiara commented on July 9th 19 at 10:58
Amateur or inaction - is almost a guarantee of losing.
The lawyer and the case quickly fell apart.
Judging by the situation you described they just can't prove anything.
Have not yet found a lawyer don't sign anything and make no statements. - earl.Weissnat commented on July 9th 19 at 11:01