This site is correct. Natacha is a pet form of the Russian name
Natalia. (In both Natacha and
Natalia, the second "a" is stressed.) A name can have several pet forms, however.
Russians often use foreign forms of the same name as pet forms. E.e. "Zhora" is a pet form of
George, probably from the French form of the same name.
If we consider the name
Natalie with its English (the stress on the first "a") or French (the stress on "i") pronunciation, Russians feel those forms as foreign. Thus,
Natalie (either English or French) can be used as a pet form of the Russian name
Natalia (or
Natalya, which is the same).