Good grief, some people do get over protective about certain places, dont they?
I reckon this person should stay in America by the sounds of what they want. Skiing in places like
Verbier and
Zermatt is hardly for the faint hearted or beginners, so maybe they just think Switzerland looks gorgeous (which it is).
ISE you said yourself that those resorts were not ideallic for this person, and you are right. So maybe its time for them to lose the hang up with Switzerland.
They want ski in/out, beginner to intermediate slopes, a 4 man accommodation (this will be exceptionally hard to find unless they are happy in a small cramped apartment for the budget they are talking about), and east lift access (you can get that anywhere in Europe to be honest, if you are lucky enough).
My suggestions would be forget Switzerland altogether, and look for a resort irrespective of nation where this looks the most likely. From what I know, this would lead me to suggest:
La Plagne (France)
Les Gets (France)
Val Thorens (France)
Serre Chevalier (France)
VT I have been to, Serre Che I plan to, and La Plagne and Les Gets are places friends of mine have been to recently, and I know they will offer what this person is looking for.
I am sure there are plenty of others, but thats my suggestions to be considered.