The Prime Directive definition from "Bread and Circuses" seems to be quite an anomaly in general TOS terms. Remember that in "A Private Little War", the backstory also had Kirk freely discussing outer space, the Federation and whatnot with primitive locals, back when he was a lowly Lieutenant and not even in charge of the contact mission...
So we're probably grossly misunderstanding something about "Bread and Circuses" here. Let's review the actual dialogue:
Kirk: "The SS Beagle was the first ship to make a survey of this star sector when it disappeared."
Spock: "Then the Prime Directive is in full force, Captain?"
Kirk: "No identification of self or mission. No interference with the social development of said planet."
McCoy: "No references to space, or the fact that there are other worlds, or more advanced civilisations."
Now, obviously we aren't hearing the full content of the Prime Directive, but just the parts relevant for the mission at hand, in suitably abbreviated form. It would still seem that the reason for full PD here is that the local culture has not been spoiled by interstellar contact yet, as far as our heroes can tell. (Of course, that's a pretty arrogant claim to make, as all they could possibly know is whether the Federation has contacted these folks before; the Federation should certainly not be the only player out there, not even from Kirk's early viewpoint!)
Then again, the idea that these rules would apply to "contact" is not supported by dialogue. Kirk is not about to make contact of any sort. He's infiltrating, in secrecy, incognito, quick in-and-out. Quite possibly very different rules apply when the mission from the very start is intended to result in actual contact between cultures - and we see often enough that the TOS-era Federation is quite willing to make contact with spaceflight and pre-spaceflight cultures of all sorts, often against the will of said cultures.
So "Errand of Mercy" is not out of the line here, by a long shot. "Bread and Circuses" is more neutral on the subject than first appears, too. "The Apple", the only one where our heroes really worry about cultural contamination, may well represent a very special case. And even there, Kirk was under explicit orders to investigate the local culture. And Spock doesn't object to Kirk spoiling a pristine culture - he objects to Kirk imposing his own human values on an alien culture that in Spock's opinion is doing just dandy on its own values. That
is what the "Non-Interference Directive" (which may or may not be the same as Prime Directive and/or General Order 1) appears to regulate.