Just offering my opinion.  There is no such thing as "concrete proof" that can't be disproven in this case due to the complexity of SEO.

Every factor is just one among many.  So a site that has "proper" URL syntax can easily and readily outrank and outperform a site that doesn't if enough individual factors across the whole spectrum are strong enough.

Conversely, A site that has numeric URL structure and "non-ideal" syntax can also easily and outrank / outperform a site that has "proper" URL syntax if that site has enough strength from other factors to outweigh the "proper" structured URL site.

Anyone who has a case study claiming otherwise is not acknowledging how complex the reality of what we do is, and how any sub-group of signals can be so strong as to far outweigh any other sub-group of signals.

I'll just add that Yahoo closed the Yahoo Directory down last year.

Screaming Frog is my go-to crawler.  One of the many data points it provides is page level. Level 0 is home page, level 1 is one-click from the start, etc...

It's an invaluable tool for anyone wanting to check on a vast range of crawl efficiency and SEO factors.

http://www.screamingfrog.co.uk/seo-spider/user-guide/tabs/

Harald,

I need to challenge your response here.

You stated:

"Boost works not only for manual actions but also for algorithmic problems, like Penguin."

That's absolutely not possible.  Penguin is not baked into the main algorithmic process. it's a separate entity that only runs a couple times a year.  So unless the clean-up was done literally within a few days of the next Penguin update, the magic recovery you claim was NOT due to Penguin related problems.