Sorry to hear about your DP's experience, goingback. It certainly was unpleasant and completely unreasonable for that part-time employee to report him for this.
He did not do anything wrong there. He sounds reasonable and measured in his response, and absolutely no one has to accept having identity labels foisted upon them - in the workplace no less - if that is not how he or she identifies.
Whether something might happen depends on what's going on at his workplace, but I would hope not.
First of all, if he hasn't done this already, ask him to write down his recollection of the conversation. In as much detail as he can remember. The longer you wait with writing or recording something like this, the fuzzier the details get.
Don't send this to anyone though, this is for his own records. If he is officially asked to respond to the complaint, follow his employer's procedure to the letter. Document every meeting and phone call, preferably by recording it (openly). If that is not permitted, ask him to take notes or minutes or ask for someone to accompany him or listen in as a witness. Then summarise what was said in an email, send it to the complaints handler and ask them to correct any mistakes he might have made in summing up. This is a technique to use when people try to avoid having any written record of what was said, so they can deny it afterwards. Having this kind of email trail makes it easier to provide evidence later (if that is needed).
This might not be necessary and he probably knows all this already, but just in case this goes further, it's a way to protect himself. HR can sometimes be bamboozled by hyperbolic complaints like this and anxious to do the right thing, lest they be accused of a ~phobia themselves, they may reprimand an employee when that isn't warranted.
And if that was me, I would have an explanation ready as to why I do not identify as cis (implies a belief in this ideology, implies an acceptance of all the sex stereotypes and sex role stereotypes associated with one's sex etc) and why no staff should be labelling colleagues in this manner. This is a belief system, and just as with any faith, I would reject being labelled against my wishes in accordance with the tenets of their faith (such as calling a non-believer an infidel or a heretic). It's simply not respectful.