I've always had this in my head as a historical fact about ww2, but recently I came upon some people (that were admittedly ussr sympathizers) that claimed that it was exaggerated. Is this true?
You've come upon a few linked matters that do have some truth to them, but indeed tend to be exaggerated. "Not one step back" is part of the text of Order 227 and is the general Soviet sentiment behind the Battle of Stalingrad. Beyond that, things Get Complicated. u/Georgy_K_Zhukov addresses the myths that have sprung up around the implementation of Order 227 and the effects therefrom. (Zhukov links to it in the answer, but Wikisource has updated the page and thus broken the link, so here's an updated link to the translated text of Order 227.)