Many textbooks use DOCHIRA (which one = formal version) and they don't teach DOCCHI (which one = informal version) like you said.
But it doesn't mean DOCCHI shouldn't be used to people who are in higher status. If you add DESU after the question word, it sounds polite enough. Also Japanese people use DOCCHI more often. That is why YesJapan uses it.
1) どっち？(DOCCHI) = Which one? (Informal) ２）どっち ですか。(DOCCHI DESUKA) = Which one is it? (Polite) ３）どちら ですか。(DOCHIRA DESUKA) = Which one is it? (Formal)
Japanese announcers may have been taught to use DOCHIRA on TV because they need to use honorific (proper) words and expressions to their guests. But in daily conversation, DOCCHI is used more often.