Westinghouse and NBC had a somewhat tenuous relationship for a long time.
In 1955, NBC and Westinghouse exchanged their TV and radio stations in Philadelphia and Cleveland. Philadelphia was the nation's third largest city at the time, and NBC wanted O&Os there. The company made a deal that was basically extortion, telling Westinghouse, "If you don't sell, we'll drop the affiliation from both of your Philly and Boston stations." So Westinghouse's KYW and WPTZ (TV) in Philadelphia came under NBC ownership as WRCV and WRCV-TV; NBC's WTAM and WNBK (TV) in Cleveland came under Westinghouse ownership with the KYW calls. A short time later, Westinghouse cried "Foul" to the FCC over the deal. Ten years of legal battles ensued. KYW-TV did very well during that time, Westinghouse pouring money into the Cleveland station, establishing "The Mike Douglas Show" there and pretty much turning the station into the focal point of its expanding empire.
In the meantime . . . In the 1950s, all of Westinghouse's radio stations, with the exception of WOWO, were long-time NBC affiliates. (Indeed, Westinghouse was originally a part-owner of the network.) In 1957 Westinghouse, which wanted to expand its broadcasting operations, dropped the NBC connection ostensibly in order to focus on local programming and to create its own news operation, but probably in part to retaliate for NBC's shady dealings with them. NBC/RCA was not at all happy over this; it meant the loss of several major-market clear-channel affiliates. In addition, as has been said, the Westinghouse TV stations that were NBC affiliates --- KYW and WBZ --- were not clearing certain important chunks of the network's programming.
In 1965, the station swap was reversed by order of the FCC. NBC made no money on the deal. KYW and KYW-TV were moved back to Philly (along with Mike Douglas); the Cleveland stations, now back under NBC ownership, altered their call letters to WKYC and WKYC-TV. (WKYC, while becoming an NBC O&O, retained KYW's Top 40 format as well as its air personalities, IIRC.) As a concomitant of this reversed swap, though I believe not officially part of it, there was a proposal that WBZ-TV would drop its NBC affiliation and join ABC, while NBC would purchase WNAC, WRKO-FM and WNAC-TV, making them NBC O&Os. The deal fell apart at the eleventh hour. The FCC may have had something to do with it, but I don't remember.
I DO remember Captain Bob being on NBC's Saturday morning lineup, and I remember The Tonight Show being carried by Channel 5 for several years. Even as a young kid I thought those were oddities.
IIRC, even after WBZ-TV picked up The Tonight Show, it didn't clear the first 15 minutes of it (11:15-11:30), which I would enjoy watching on WJAR or WRGB.