Il problema era nella stringa di connessione. In particolare, avevo le proprietà "Nome applicazione" e "App". Una volta rimossi, ha funzionato.
CATTIVO:
<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" />
BUONO:
<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" />