I think it's more a case that technically, when making first contact with a new world, The Prime Directive temporarily always applies until a survey can be conducted to see if enforcement of it for the new planet in question should be maintained.
The above said it's kind of interesting in that to do the planet survey, The Federation representative in question has to break the Prime Directive to arrange for the planet survey. Remember that Tyree knew all about Kirk, and the Federation; but promised silence after Kirk left.
We can interpret all the cases in the terms of the relevant TNG episode, though: yes, there is always a survey to determine how much sheltering from truth the natives need , but it's a covert survey.
Kirk visited a planet inhabited by near-humans. He could have done so pretending to be one of them. Tracey, likewise, no facial reconstruction surgery required. SImilarly, Sulu conducts a preliminary survey on Beta III in native clothing. All we have to assume is that the type of clothing appropriate for Omega IV would allow Tracey to wear his full uniform underneath. Or perhaps even invite him to do so - perhaps he scanned for native garb and saw Yang furs, and decided that those would not only conceal his gold shirt, but would itch like hell without it?
The time for revelations would come late in that particular game. In some cases, perhaps never. We don't know for sure when and why Kirk revealed the truth about himself to Tyree, say, but we can postulate he wouldn't have yet something forced him to.
If that's the Federation's SOP in the 23rd century, what happens if the person or persons who are aware of the Federation representative's true origin decide (for whatever reason), to break their promise and reveal that their Planet was visited and surveyed by a being or beings from another world?
Kirk goes to a penal colony.
Except he never does*, so presumably it's not that big a deal: most surveys might conclude in a verdict of "We'll protect them for now, but since we found them, others will as well, and soon, so we'll keep the champagne cool and the dress uniforms well ironed".
Timo Saloniemi
* Actually, Kirk is awfully familiar with penal colonies. Perhaps he's a regular customer, due to his relaxed attitude towards the rules of pre-contact surveys?