My personal experience - I'm currently in the 142 training environment so I have a ton of corporate contacts. I usually get the "fast track" info when a job becomes available. Have interviewed many times in the last 3 years and made the short list only to get rejected on the currency/recency of experience issue. Even personally know - outside of aviation - a couple of major aviation department directors. Was negated for those jobs because of recency and not typed in specific model of Gulfstream they fly (although I am typed in the G-IV).
I believe in the 'good ole days' it was a "this is a great guy so we will take a chance even if he's not typed." Now, if you don't have a type, 500 hours of PIC, and recency of experience, IMO you're toast (at least for the Fortune 50 jobs).
Additionally, my experience with these companies has been they don't use the "head hunter" method. They have company websites with thousands of candidates that have pre-registered to get notified when a job becomes available.