They got away with it because there was probably no reason to coubt her word when she aplied for the second marriage. She was still young and the register office would have had no reason to doubt her and no access to any records in another RD,.
Internment was ay White City dog track and it was a desperate and cruel time for any German citizens which is why there was a desperate rush or obtain nationalization papers, however , there is no record that Franz did that.
The little boy was Alfred not Albert BTW. i don't believe that Alice was pregnant when she married Fritz in 1912 as the baby was not born until 1914 but by the time the baby died in 1915 her husband could well have been interned or had left England of his own accord, i don't think there is any instance of the surname in English records even in the immigration
however:
Kriegsranglisten und -stammrollen des Königreichs Bayern, 1. Weltkrieg 1914-1918 Bavaria, Germany, WWI Personnel Rosters, 1914-1918
Name: Balthasar Freidhöfer
Birth Date: 26 Jan 1878
Birth Place: Heiligenstadt Bamberg Bayern (Bavaria)
Combat Arm: Infanterie
Type of Unit: Landwehr-Infanterie-Regimenter
Unit: Bayer. Landwehr-Infanterie-Regiment Nr. 7 (Bayreuth)
Volume: 3703. Kriegstammrolle