The problem with unit test as documentation is that over time they end up reflecting the same misconceptions that the code has. Someone does a refactor, misunderstands how the original code works, and "fixes" the unit tests to pass. Now you have tests that lie just like comments can lie.
By contrast, I have really never seen truly self documenting code. The comments may be up to date by virtue of not existing, but the end result is just more confusing. YMMV
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.