It is working now!!
I could realize that some users were connected in their iCloud, but they needed to perform the second verification factor (related to the password of their apple ids). Those users without the second factor confirmed, they did not save new data in RecordTypes. They got only to read data. After to confirm the second factor users are using the app as previously.
In either you simulator or your iDevice, go to settings and sign-in to Apple's iCloud. Users are not allowed to write (CREATE) to CloudKit databases unless signed-in.
Signing-in, via Settings, will get rid of 10/2007 "Permission Failure" "CREATE...." error.