There's more to any apparent difference in the quality of open source code than just deadlines. It's also things like survivor bias. Messy open source codebases don't attract contributors at the same rate.

And deadlines are still a part of open source software development. Most the really widely used projects are heavily supported by corporate patronage, and you'd better believe that those companies are creating deadlines for the people they pay to contribute to those projects based on their own business needs.

For my part, to me it seems that "enterprise vs non-entperise" is a better predictor of code quality than "closed vs open source".