Please be kindly advised that the warranty of your Honda e may be invalidated if a damage is caused by using third party chargers.
I think their response is poorly worded, but I have seen similar (and reasonable) statements over the years in other spaces. I also think "may" is doing a lot of work in that sentence, which is why I've emphasised it. It's not "will".
Tesla only needed to test their chargers with Teslas, and Tesla cars (let's assume) accept high voltage and current from the off. So if they properly negotiate with the car and agree 100kW (or whatever) in the right way, that's great. If they don't, and just immediately apply a high voitage with no current limit then that's blatantly unreasonable (in CCS2 terms) but perfectly functional (in Tesla terms). In that scenario, you can argue the toss as to whether it's Tesla's fault for offering a charger which isn't compliant or your fault for using it, but were a car manufacturer to say "we're not paying, you can bring a small claims action against the charger supplier" they'd be within their rights.
If Tesco (as happens on occasions) put diesel in the petrol pump and you fill up with it, Ford aren't paying for the damage to your engine. But you have an open and shut case in a small claims court against Tesco. It's not obvious why this scenario is substantially different.
Tesla rolled out in 15 obscure locations in part to gauge demand and impact on their own users, but I don't see that side of the trial delivering terribly interesting results. I'm an M40 regular, and I'd consider using Tesla chargers at Cherwell Valley, but I'm hardly doing to shlep to a trading estate outside Banbury to use one there, and nor are many of Elon's customers. But given Tesla's...looks for euphemism...considers whether he wants to be sued..."robust" attitude to public relations, I can quite see them using those 15 sites as a beta programme to find out which cars their chargers blow up, and accept that they may take some PR flak for it.