Don't worry about translations, top right of the Gemeinsame Einrichtung KVG site there's a language selection button, English included. This part is very interesting:

https://www.kvg.org/en/domicile-in-s...--1--1077.html

So, that organization is telling not my problem, we'll check if it works after your reimbursement request. In practice, it means that the EHIC works as a bail when you go to the hospital/doctor. You get the service, leave there without paying nothing at the moment, but the question of who pays? is answered later.

There may be potential for health insurance arbitrage, or not.

In any case, it is unlikely that a person employed by an entity in a poorer EU country (and receives their local salary), would be deemed to earn enough to be issued a permit to live in Switzerland.

The rules are the same for the whole of Switzerland, it is just that the above cantons/cities provide for an exemption form request online directly from the KVG common institution.

In all other places, the request must be made directly to the respective cantonal health insurance authority that is in charge of issuing exemptions.

This is correct.

In any case not paying on the spot after treatment is also applicable for KVG insured people, they typically get a bill after the fact either directly from the medical institution or from the health insurance company.

Whether the quality of the treatment is the same as with KVG is a different question. In some hospitals there is a separate section with separate doctors for patients with no cover or with an EHIC.

That's a new thing for me. First time I read about 1st and 2nd class health services in CH.

Would create a lot of drama if it ever comes to light, especially with the lack of transparency in the way some doctors and hospitals charge health insurance companies their time.

So, a conspiracy about the quality of services offered to people with EHIC cards?

No, real life practices in some hospitals for people with no cover (think Romani people) or those insured by another state (EHIC) with separate waiting rooms and separate doctors (often more junior).

Nothing stops medical institutions from doing this, you get what you pay for.

Assuming there are effectively 1st and 2nd class health services and nothing stops hospitals from doing this, why recommend the EHIC alternative with rather significant caveats?

Your kid broke an arm playing with friends? No local health insurance? That door please...

Because paying for a KVG insurance when you are already paying for German social security costs on a Euro salary and living in Switzerland is not ideal.

If you see my initial posts it was merely a suggestion hence the '(if you so wish)'.

It does not work that way, first of all the kid would be insured via KVG as the father (OP's husband) would be working here.

Secondly, people with EHICs would never be refused treatment, all I am saying is in some hospitals (notably high-cost university hospitals) there is a separation of care.

trolling =/= bullying

You claimed categorically that OP's medical bills will be covered by her German health insurance. Please provide an official German source confirming your claim both for German public health insurance as well as private health insurance (GKV and PKV, respectively).
(For those wondering, PKV is available if you earn more than ~65k Euros, though you can chose to remain insured under GKV)

Germany's health ministry explicitly states that only costs with a domestic origin are covered, treatment, care, drugs, etc. The exceptions don't apply to people residing abroad, they're basically the already mentioned emergencies for tourists abroad.

What you provided so far is a Swiss entity saying "we'll try to charge the insurance abroad", but the real question is whether that foreign insurance is willing to shoulder the costs in the first place.

The link you provided is for tourists, so not relevant here.

I refer you to a previously quoted post:

Art. 2 Ausnahmen von der Versicherungspflicht

1. Es unterstehen nicht der Versicherungspflicht:

d. Personen, die nach dem Freizügigkeitsabkommen sowie seinem Anhang II, dem EFTA-Abkommen, seinem Anhang K und Anlage 2 zu Anhang K oder einem Abkommen über Soziale Sicherheit wegen ihrer Erwerbstätigkeit in einem anderen Staat den Rechtsvorschriften dieses Staates unterstellt sind;

1. it is not subject to compulsory insurance:

d. Persons who, under the Agreement on the Free Movement of Persons and its Annex II, the EFTA Agreement, its Annex K and Appendix 2 to Annex K, or a social security agreement, are subject to the legislation of another state on account of their gainful employment in that state;

https://www.fedlex.admin.ch/eli/cc/1..._3867/de#art_2

as well as he agreement on the Free Movement of Persons between Switzerland and the EU (annex II of the Agreement on the Free Movement of Persons, art. 17, 24, 26 Regulation (EC) No 883/2004, art. 24 Regulation (EC) No 987/2009)

I don't know why it is relevant to change the question around. Whether or not the Swiss KVG common institution is successful in claiming costs from Germany has nothing to do with OP and OP would in no case be liable for medical costs as they are insured via their German EHIC.

Correct. Please provide one that does apply and corroborates your claim. A German one, that is, not a Swiss one.
It would help if you read your own links. The KVG says in your own link

Any German link is irrelevant as OP would be resident in Switzerland, not Germany. But feel free to look up the already provided European legislation (which is relevant in this case):

Free Movement of Persons between Switzerland and the EU (annex II of the Agreement on the Free Movement of Persons, art. 17, 24, 26 Regulation (EC) No 883/2004, art. 24 Regulation (EC) No 987/2009)

Yes, maybe you should read more closely:

This means the KVG common institution will not cover costs unless you are insured by an EU/EFTA member state i.e. without an EHIC card and S1 form they will not underwrite bills. It does not say the patient is liable for costs if the KVG common institution does not manage to have costs reimbursed from the country.