This is the correct timeline. Penn State was voted down by one vote (5-3; apparently that was the score of all five votes on the matter).
Georgetown, Syracuse, Providence & St. John's met to found the conference... initial invitations went out as follows:
Boston College (over Holy Cross, UMass, and BU)
UConn
Rutgers (declined to stay in the A8 (now A10) with Penn State) -> Seton Hall selected instead
Villanova was added a year later over Temple & St. Joes.
Then the Penn State decision came up. It's been widely reported the three no's were: Georgetown, St. John's & Villanova which had recently killed it's football program.
Pitt then was added to protect the league; kill Paterno's Eastern sports conference and retain Syracuse and BC.
Sources: Crouthamel's Big East History, Tranghese's NYT interview, assorted other sites
There are varying accounts, but the decision was as I initially characterized it: The Big East had a choice to add Pitt or Penn State. Pitt was favored as the better basketball program in the city market. Here is an account as you referenced:
Syracuse's Crouthamel explains what the Penn State application meant to the Conference:
"After only two years of existence as a conference formed specifically for men's basketball, football became an issue. Joe Paterno, head football coach and then Director of Athletics at Penn State, had been trying to put together an all-sports conference of the eastern Division IA independent schools. They included Syracuse, Boston College, Pittsburgh, Rutgers, West Virginia and Temple. While our football fortunes would be well served through such an alignment, it would have been a step backward for men's basketball. To enter into such an alignment, Syracuse and Boston College would have had to leave the BIG EAST. With the reluctance of B.C. and Syracuse to do so, Penn State then asked for membership in the BIG EAST. This was a turning point in the Conferences history. If Penn State was accepted, our football would be protected. If Penn State was rejected, B.C. and Syracuse might have no other option but to leave the BIG EAST, and join together with the other Eastern independents. To expand membership in The BIG EAST Conference, six affirmative votes were necessary. The vote was 5-3. Instead of taking Penn State, we invited Pittsburgh as the ninth member. At that time Pittsburgh and Penn State were bitter rivals, and Pittsburgh was less than enamored with aligning itself with Penn State. Pitt's membership in the BIG EAST, along with B.C. and Syracuse, checkmated Penn State's eastern all-sports conference, and gave the Conference one more Division IA school. This football issue nearly caused the premature demise of the BIG EAST. Clearly, three schools in the BIG EAST had no concept of the importance of football, but the others realized that this decision not to invite Penn State would come back to haunt us. In fact, football would dictate every future consideration of membership expansion of our 'basketball' conference."
Joe Paterno and his school needed six votes, and he received five. There is still controversy about who the three no votes were, and former Big East Executive Director Mike Tranghese said that Syracuse voted for Penn State.
Who were the three?
Paterno always believed that Boston College and Syracuse blackballed him, with the help of the Pitt administration.
The person whom Paterno blamed for the Big East rejection was Ed Bozik, an ally of Chancellor Wesley Posvar who became A.D. in Sept. 1982.
Bozik's tenure was controversial, but in his obituary in 1994, this line appeared: "Bozik was given much of the credit for Pitt's move into the Big East Conference in 1982."
In short, he was the man whom Paterno accused of arranging the blackballing of Penn State in 1982.
The galling part is that instead of Penn State gaining a spot in the Big East, that spot went to Pitt.