What is the best metric the press could use for measuring private companies' success? Money raised and number employees might be bad, but I'm not sure they're not also the best ones possible.
Quantcast is a good start, though certainly not perfect and requires opt in from the company. Then there's the whole mess of Comscore, Compete, Google Analytics, etc. Ask 5 companies to measure one site's traffic and you'll get 10 answers.
My point wasn't that there aren't other tools to measure success, but that blaming the press for funding and headcount being emphasized is silly.
Edit: There's no shortage of traffic data in the press either.
One is a count that is likely in the millions or tens of millions of people and made up of nearly-anonymous people from around the world. The other is likely in the tens and made up of people in a single building.
A journalist could come to your office and make a pretty good guess at how many people work there. That's not to say people don't lie about it, but I think it's reasonable to expect an independent third party to be able to roughly figure out how many people work at a company even if the company wants to lie about it. I don't think it's reasonable to expect the same with web traffic.