Mr Jackson soon retracted his comments and RadioLive issued a statement saying that his comments should not be taken as a call for violent action.
In its findings, the BSA said Mr Jackson's comments were "extreme" and advocated strong industrial action.
But it ruled that most listeners would have judged the broadcast to be a "good-humoured, provocative verbal sparring".
"It was a kind of letting-off of steam," the BSA concluded.
"It was not serious advocacy of violence. It was the sort of ranting that our society is willing to allow and not take seriously, particularly on talkback radio."
The BSA took into account Mr Jackson's retraction and explanation and found that listeners had not been encouraged to break the law.
Mr Jackson described the ruling as a "victory for the right of free speech and common sense".
"When you're in the heat of a debate with your mate, you get a bit carried away ... but it's talkback for goodness' sake. Sometimes you say things you don't mean," he said.
The broadcasting watchdog also released its annual report today, which showed that it received fewer complaints than last year.
The BSA received 195 complaints and issued 162 decisions, compared to a record high last year of 236 decisions.
"We believe that if the system is working well, complaints will drop over time," chief executive Susan Freeman-Greene said.
"The implication of this is that broadcasters breach codes less often, the public are better able to identify breaches and the broadcasters' own complaints processes are more effective, prompting fewer referral to us."