It's true! Landline phones on copper POTS (plain old telephone service) lines often still work when the power is out because those lines carry their own low-voltage power. Sadly, phone companies are ripping out copper phone lines like crazy and replacing them with fiber optic lines that don't carry their own power, so this may not be true for much longer.
I learned this by growing up in rural Texas where power outages were frequent but the phones usually still worked. 😄