It depends upon a fact about what we mean by survival rates.

In most cases survival is defined in terms of fraction of population who are alive after a set period of time from diagnosis.

Suppose Bob is going to die of Foozle cancer in 2025. If I diagnose Bob in 2019 he gets more than five years survival. If my diagnosis method only catches it in 2023 the survival rate looks much worse. But all that changed is when I told Bob he's going to die.

In contrast if I develop a treatment for Foozle cancer, maybe Bob doesn't die until 2030. He's survived more than five years after diagnosis again - but this time it's because I was able to actually help.

You're forgetting a much simpler scenario that could wildly throw off survival statistics: early detected cancer might have a chance of never actually killing the patient even without treatment. Therefore early detection increases survivability in the statistics because it's counting more "duds".