A lot of the "interference" Kirk does is in situations that he was already thrust into. Also, he was frequently dealing as BillJ mentions, with cultures that were already "contaminated," so Kirk felt he had wide latitude to act in the best interests of that culture.
And it should be repeatedly pointed out that the PD has been written as wildly inconsistent. The TOS PD is NOTHING like the TNG PD. It's much more flexible and it allows for helping primitive societies at risk from natural disasters.(TPS) Even the PD in modern Trek has not stayed consistent within its own era, so judging Kirk's actions by the ludicrous TNG-era PD is unfair.
As it happens I agree, I too think TNG position was too liberal, as are our own laws. The ideal is probably somewhere in between.