Yes, I've read the report and I'm also aware of how airlines can appoint AMEs.
You still haven't answered how you prevent a pilot who is really determined from hiding aspects of his/her medical medical history from his AME and/or employer.
Lets imagine your plan is enacted and "my" company ( or even my national Government) insists I go to doctors appointed by them for any medical consulations and Class 1 renewals.
Lets also imagine I have a temporary condition I don't want my company or AME to know about.....I could simply get it dealt with by another doctor not connected with the company, and in fact one who may not even be in the same country or even continent as the employer. If I don't tell the treating physician about my employment and I never tell my company or AME about the outside consultation they will never be any the wiser.
Writing rules insisting pilots use company employed or company appointed doctors will not magically solve the "Lubitz" problem.