I think they are both myths!
Analytics are real eye openers, and the landing pages (at least in my experience) tend to be the content heavy pages that live higher up the google index! The Home page does still have a rightful place though, hitting “Home” at the top should give you the introduction to the service, and it will probably forever be the home of businesses carousel obsession.
I think the three/four clicks thing is something that has been passed on too - Not this report, but a quick google “3 click myth” found this: http://www.intrateam.com/da/blogpost/3-click-myth-intranets-debunked - naturally I think testing users, tree tests, etc. are good ways to make sure that your IA isn’t all messed up - but from what I’ve experienced and read, I think as long as the user gets what they want, within a reasonable time, and don’t feel lost while on the path - then it seems that clicks are not a concern.