O problema estava na string de conexão. Especificamente, eu tinha as propriedades "Nome do aplicativo" e "Aplicativo". Depois de removê-los, funcionou.
MAU:
<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" />
BOA:
<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" />
