Traditional Paladins OD&D, AD&D were L/G, drawing power from a single deity, so going undercover is not in their repertoire. They would always speak the truth (as they see it), followed swiftly by martial enforcement, if appropriate.
The modern Paladin of 5e is difficult to comprehend, by comparison, as it seems to be "some jolly committed warrior" that does not cleave to any particular deity, but receives divine power. I suppose that it is trying to encompass all forms of dedicated warriors, including what used to be the Blackguard, but does a really bad job of justifying itself.
The focus on an "oath" is pretty meaningless unless the Paladin's power in some way actually derives from the oath, but it doesn't, the power is divine, as it has always been. A better idea would have been to use oaths to bind Paladins directly to a patron, in the manner of Warlocks, which would allow "traditional" Paladins, Blackguards, and any other dedicated warrior, as well as being much more in keeping with the real-world Paladins who were the oath-bound bodyguard of the Carolingian Emperors.
WotC just made a mess out of the Paladin as far as I am concerned.
