Code that breaks is much more likely and damaging than comments that are out of date. In my life I've never had a case where the bad outweighed the good for comments.
As for the argument that it wastes time to update comments, I've never seen a codebase where the comments were so voluminous that it would be a significant burden to update them. Devs avoid updating comments because there is usually no penalty for doing so (boss doesn't call them on it, and the code still runs), and they think they've saved a few minutes when in fact they're just kicking the can down the road for the next dev who has to decipher the incorrect (or missing) comment.
And often for completely different reasons. Blithely assuming it's all about "lying" comments is totally unsupported by any evidence.