True. From a certain point of view.
Sure, that's possible and I've definitely entertained it in the past, but a couple of the novels written after Episode III was in theaters seem to strongly hint at the Emperor knowing through the Dark Side that Anakin/Vader hadn't actually killed Padmé when he Force choked her on Mustafar and that she had indeed survived for a short time after the incident. He might have told Vader that he killed her as the straw to break the apprentice's back....the moment that truly shattered his spirit and ensured his conversion to the Dark Side of the Force and to the Emperor himself.
Palpatine had to destroy the last connection Vader had to his former life even if that meant making him think he had killed his own wife. He had led Anakin down the dark path of temptation by telling him he could save Padmé from dying....having failed to do so (and making him think that he actually killed her himself) would render him a complete shell of a man that Sidious could then mold into the kind of apprentice and henchman that he needed to help rule his new Empire.
Again, these are the impressions left by a couple of the books and it all depends on if you give the novels much if any canonical weight in your view of the Star Wars
universe. I pick and choose myself but Palpatine knowing the truth but deliberately lying to Vader in order to crush his heart and spirit seems like something the Emperor would do....and gladly.