Het probleem zat in de verbindingsreeks. In het bijzonder had ik daar de eigenschappen "Applicatienaam" en "App". Nadat ik die had verwijderd, werkte het.
SLECHT:
<add name="MyDbEntities" connectionString="metadata=res://*/MyDb.csdl|res://*/MyDb.ssdl|res://*/MyDb.msl;provider=System.Data.SqlClient;provider connection string="Data Source=MyDbServer;Initial Catalog=MyDb;Persist Security Info=True;User ID=MyDb;Password=MyPassword;Application Name=MyDb.API.Models;MultipleActiveResultSets=True;App=EntityFramework"" providerName="System.Data.EntityClient" />
GOED:
<add name="MyDbEntities" connectionString="metadata=res://*/MyDb.csdl|res://*/MyDb.ssdl|res://*/MyDb.msl;provider=System.Data.SqlClient;provider connection string="Data Source=MyDbServer;Initial Catalog=MyDb;Persist Security Info=True;User ID=MyDb;Password=MyPassword;MultipleActiveResultSets=True"" providerName="System.Data.EntityClient" />