There is no national organization or "match," like you would see in the US. The system does not work that way in Germany... when a hospital has an opening for a resident (Assistenzarzt/ärztin), they simply fill it. In that regard, what you heard is correct -- you apply for a pantload of jobs, you interview wherever they offer you an interview, and you hope that your CV, winsome personality, language skills, and citizenship status are good enough to score you the gig.
There are, however, TONS of German medical recruiters who would love to talk with someone who has an EU medical diploma and can already speak German. If you get a good recruiter (and there are plenty of bad ones out there, alas), they will arrange your interviews, assist you in preparation, and they might even spring for your travel and hotel costs while you are interviewing, assuming you are not a million miles away. They also should not charge you anything... all costs are borne by the hiring hospital.
With that in mind, find yourself a good recruiter... and run the other way if they act like jerks, if they want to charge you a fee, or if you just feel like they are shady. There are plenty of good ones in Germany, and they are definitely still hiring.
