An interesting thought, yet if you're making this point, I hope you have more evidence than that. In other texts,
Sauron is frequently called
Morgoth's greatest servant. As it says in
Morgoth's Ring,
"Melkor knew of all that was done; for even then he had secret friends and spies among the Maiar whom he had converted to his cause, and of these the chief, as after became known, was Sauron." (emphasis added). Also, in the Valaquenta, Of the Enemies, it says this regarding Sauron: "[Sauron] was only less evil than his master in that for long he served another and not himself". This seems to answer the problem, but still, your point is valid and raises valid questions.