So there are a few questions depending on the answers will hopefully help your situation:
1. Who approves the hardship? Does the hardship request go through your HR department and then they send it on to the 401(k) provider or does the 401(k) provider make the determination on whether or not the hardship is approved? If this is the case, your HR department shouldn't have any reason to get involved.
2. Can the service provider, provide you a detailed statement with generic or less descriptive coding? This provider has probably had this question before especially since there can be a stigma against mental health issues. Kudos to you for recognizing the issue and being strong enough to ask for help.
If neither of these work, I would go to HR and speak with the person who handles the FMLA and or leave request. This is the designated person in the company that helps employees get approved leave for medical reasons whether it is theirs or someone in their family. Make sure you start the conversation that is regarding confidential health information and you need it to stay that way. The HR group is there to help and if your company wants to help you be successful, because it makes them successful. I suggest to keep detailed notes of the information you provide, to whom, and the date and times, so if you feel you are wronged in anyway, you have leverage. I also, think this will give you peace of mind.
Best regards and honestly I hope all goes well for you!