How do mutate and ownership rules interact?
Reminder text is not rules text. The reminder text for mutate is shortened for readability, since owner and controller of a mutate spell are usually the same. Only the Comprehensive Rules are ultimately relevant.
On reminder text:

Reminder Text
Parenthetical text in italics in the text box of a card that summarizes a rule that applies to that card, but is not actually rules text and has no effect on play. See rule 207.2.

The rules for mutate say:

702.139a Mutate appears on some creature cards. It represents a static ability that functions while the spell with mutate is on the stack. “Mutate [cost]” means “You may pay [cost] rather than pay this spell’s mana cost. If you do, it becomes a mutating creature spell and targets a non-Human creature with the same owner as this spell.” Casting a spell using its mutate ability follows the rules for paying alternative costs (see 601.2b and 601.2f–h).

The reminder text on mutate cards is shortened from its actual rules text. This has been done to improve readability and to fit the lengthy text on the card. However, when it comes to special cases, it's important to remember that it has no relevance for the actual rules.