Well that was just one hypothesis to incorporate parts of the family story shared in this thread:
1. Family story that Magda had a child by a businessman in Svendborg. Well, Magda was in Copenhagen by 1914 and Paul was born Jan 1916. Various explanations are possible - a pregnancy before Paul being just one.
2. Family story that Magda left Denmark at age 18. Well, Magda left Denmark at age 25. Age 18 could be just an error in the family story - but also age 18 could be when she left her father's home (circa 1908). The latter story fits with the records you've found - she's not with her family in 1911.
3. Family story that Magda's parents (father/stepmother) were scandalized by her or in conflict with her in some way. The records we've found seem to show that the parents would not even know Magda was pregnant when she left Denmark.
The earlier pregnancy is just an idea, and probably WRONG. Just trying to incorporate this businessman in Svendborg. Maybe that was an affair - but no pregnancy? another idea. Or maybe he didn't exist, lol.
Sometimes family stories are totally wrong, or have some mistakes in them. Sometimes they are correct! As you two already pointed out early in this thread.
Wish I was more helpful.