It was because Frank and Dean and Hef and so many others sold a hedonistic, drop out (of conventional middle-class morality), turn on (with a martini and some Mantovani) lifestyle. To most of America, the late 60s counterculture wasn't Woodstock nearly so much as it was Laugh-In.
I think Eric nailed it. Not that I was doing much in the late 60's, being in utero and all, but I fancy myself a connoisseur of bad TV and wiseguy entertainment. I have never perceived Dean Martin or Sinatra circa 1970 to have been anything but wildly popular and at maybe the 1999 Starbuck's level of popular hip (as opposed to hip hip; compare White Stripes 2004 and White Stripes 1999).
But the discourse here stems from a poor premise: that there is one kind of hip. I 'm sure that the sight of Sinatra or Martin or, probably the greatest single entertainer of all time, Milton Berle, churned stomachs in Haight Ashbury, Madison and Berkeley for a long time. But in a different milieu, I submit, these characters never became completely unhip. There is principled counterculture, like that of the sad tie-dyed deadheads that make Haight fairly less hip than your average Wal-Mart, and then there are the amorally hip. Those who sell licentiousness, graft, and violence below the surface of popular consumer culture as hip. As long as these people actually associate with the truly dangerous and objectively counter-cultural (e.g., Momo Giancana), their nihilistic hipness is largely assured. This kind of hip tends to age more gracefully, with the pitiful exception of Hugh Heffner. And, of course, sometimes, the nihilistic hipster becomes confused, trying to portray the principled hipster and/or the pop-culture hipster playing himself, as opposed to playing the system. See Henry Rollins.
I get violent when I'm f**ked up
I get silent when I'm drugged up
Want excitement, don't get none, I go wild
I don't know what can be done about it
If you play the game you get nothing out of it
Find out for yourself try bein' a goody goody
You better cheat cheat
No reason to play fair
Cheat cheat or don't get anywhere
Cheat cheat if you can't win
(Strummer/Jones)