Wow. I’ve never had to show ID at Dutch hospitals or clinics. My GP does the referral (!!! great GP!!!) or I turn up at A&E and the (medical) intake has begun. I speak Dutch though, maybe that makes a difference?
In many (?) hospitals, you need to take your ticket somehow when you enter. You can sometimes do this with the letter or email you got, but you can also scan a (Dutch) ID. See 'aanmeldzuil': https://www.zuyderland.nl/ziekenhuis/afspraken/aanmelden/
tergooi MC in Hilversum has no one to talk to when you walk in, really. You get a ticket with your Dutch id, wait where it tells you, and someone calls your name. It's really efficient if you have Dutch id!
At least when I was there last year, if you head left from the entrance there's a couple booths there. Usually at least one is staffed.
Also if I remember at Tergooi MC you needed to register in their system anyways before an appointment. In the past they issued a little plastic card at the very same booth.
Thanks! I called them last week and they told me I couldn't do anything without a specifically Dutch ID. ISTR seeing booths with no staff in the past, I will look again next time.
It could be they were referring to DigiD for logging into their online portal. I recall needing to use it to schedule an appointment with a specialist.
Inside the hospital itself you should be fine with an EU ID card or a passport, I don't think they specifically need a Dutch ID.
Edit:spelling and clarification on intake