As OP has already established, there's a phrasal verb to water down (literally and figuratively, to dilute). But that's not relevant to the cited usage here, where it simply means to [make] wet. Per my comment, this is clear from the context, which explicitly says that the roads were dampened to reduce the dust.
OP is correct in supposing that down in this instance simply refers to the fact that the water is splashed down[wards] onto the road. But I think it's fair to say the semantic content of the word is negligible here, since the meaning should be just as clear even if it's omitted.
Taking a different verb, it can be seen that [optional] prepositions are often added after common verbs of action where the [minimal] semantic content of the preposition can be largely ignored...
He ate his tea in a hurry, brushed up his jacket, and started off.
The man lifted himself off of the ground, brushed off his jacket and walked away.
He stood before the mirror while his valet brushed out his jacket.
In those examples, native speakers would be unlikely to register any difference in meaning if those prepositions were transposed - or more importantly, if they were omitted altogether.
In my examples, to brush up can sometimes be a "phrasal verb" (to review; refresh one's memory) - but that clearly doesn't fit the context, so it can be discounted.
My advice in such contexts is to consider the possibility of a phrasal verb usage, but if that doesn't quickly suggest a credible interpretation, assume the preposition isn't particularly significant. Often it'll be an almost random choice (but don't add such prepositions yourself unless you're familiar with the usage).
OP's context is an example of OED's definition #3 for the phrasal verb to call out (first recorded 1823)...
To challenge to fight (esp. a duel).
It's effectively a figurative extension of usages such as...
"Come outside and say that!" (repeat your insult, and we will fight where it is more convenient)
...but the modern usage doesn't directly refer to fighting with duelling swords or fists. The metaphoric "weapons" which will be used in the "contest" are justifications (facts and logical arguments).
By implication, the person issuing the challenge expects to win, because he doesn't think the other person actually has valid justification for whatever he said, implied, or did. It's important to note that you can just as easily be "called out" over disapproved-of action (or inaction) as a disputed statement...
"If your husband never helps with the housework, you should call him out about it."
That's to say, to call [someone] out over/about X means to demand that they justify X.
Best Answer
Taking the sentence as a whole, the texter feels that full disclosure is very important. Therefore, a text was issued. The text was issued in the spirit of the perceived requirement for full disclosure.
In other words, an act performed in the spirit of something is done because the something requires it. The reason given is often moral, as it is in the example.