The "forget the resume" part, or perhaps the "we don't believe in years of irrelevance" -- they believe 6 months and 5 years of experience are roughly the same when it comes to productivity.
By all means, write a good cover letter -- but be aware that apparently unlike 37signals, some hiring managers do actually skim resumes when making the first cut. I'd feel irresponsible not doing so.
"Write a good cover letter", however, is not particularly novel or link-bait worthy advice.