thank you for sharing this rather theoretical question with the wefugees community.
You are right, according to Dublin III regulations, Germany would be responsible if the EU is entered via Germany visa-free or with a German Schengen Visa. But every Country has the right to take over the asylum procedure (Selbsteintrittsrecht der Länder). this is stated in Artikel 17 of REGULATION (EU) No 604/2013 (Dublin III)
"Any Member State should be able to derogate from the responsibility criteria, in particular on humanitarian and compassionate grounds, in order to bring together family members, relatives or any other family relations and examine an application for international protection lodged with it or with another Member State, even if such examination is not its responsibility under the binding criteria laid down in this Regulation"
I hope my answers were helpful and I would be very happy if you would contact me again with further questions. I'm a consultant with mbeon and I‘ll be glad to help you over a longer period of time. Mbeon is an online advice for migrants via the mbeon app, which you can install on your smartphone for free. Download it from App Store or Google Play Store. You can find me in the mbeon app and get confidential individual advice in a secure virtual space without other people reading our conversation. Further information: www.mbeon.de.