I'm curious where you found that misleading information in the Aegean app. I'm in the app now, and when I'm going to "How to earn," I get a table where it clearly states under Lufthansa: "Note: Miles cannot be earned in booking classes O,I,X,R,N,L,T,E,K,P,F,A,G."
Also, Edelweiss is not a part of Star Alliance. Within Star Alliance, it's metal that counts, meaning that you will normally not earn any miles if a leg is booked under a Star airline but flown by a non-Star airline.
On a sidenote, I discovered today that ET also has business fares in P which earns 0 in M&B.