No, you're right in that respect. My point was that EHIC doesn't provide routine health care, just emergency treatment. Even then, if you've been present for a long time (I think it's 18 months) then a sharp hospital employee might realise that even your EHIC cover has expired.
If you needed a substantial course of therapy (say) you'd have to pay for it or return home to get it, unless you have S1 cover. (EHIC also covers Norway, Switzerland, Iceland and Liechtenstein).
Yes that is what I thought, I used EHIC when I mean't S1 cover which is certainly what a lot of expats particularly the elderly or with a disability are worried about losing because of Brexit.