My take on an explanation:
Hazou & Co are traveling through several reasonably dangerous areas performing odd-job missions any one of which could escalate into a serious fight. They have genin-ish tier combat capabilities and Minami is one of their only all-rounder chunin assets. A split second of hesitation on "should I or should I not reveal this technique to my presumptive ally" could easily result in death. Given these circumstances, leaving out such a crucial ability as Noburi's Mist draining seems extremely optimistic. How would the team actually know that the thugs were mortals and not ninja in disguise, for example? It does not make sense to use anything less than absolute force when dealing with unknown enemies, unless one has Orochimaru-tier defensive capabilities.
A series of 10 missions with 95% survival rate is just as dangerous, if not more so (due to complacency / fatigue) than 1 ~50% Arikada-tier mission.
The long-term is important. But to get to the long-term, you have to survive the short term. Presumably Leaf needs these messages delivered safely and effiicently. The damage to Leaf from Hazou & Co being disappeared via ambush or unforeseen circumstance is massive from both a logistical and informational standpoint, to say nothing of their skywalkers.
If Jiraiya pulls this off, they are clan of the Hokage. Whatever concessions Minami would extract in exchange for her silence would be miniscule next to the influence gained. In that light, the absolute highest priority should be survival now, followed by reasonable execution of their mission. The maximal chance of 'preventing skywalkers from falling into enemy hands' alone would justify the disclosure if it made the team even 5% more effective overall.
Perhaps Hazou did not explicitly think these things, but it seems possible that they were present in his general 'intention' in how he acted. I do feel that the way Hazou's clan members acted evinced a confidence in their safety that bordered on outright arrogance, given how paranoid about physical safety they were just two months ago. They are way too concerned about the medium-long term and not enough on short-term survival. This is still an elemental nations on the brink of war with random squads of S-class missing-nin running around unchecked. Have the party members forgotten that a single roll against a jounin will instantly TPK the entire party?
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Somewhat unrelated, but thinking on it further, I do not see how it is realistically possible for ninja to go on an even "kind of dangerous" mission together without revealing more-or-less their full capabilities to their teammates. They would be massively outcompeted by ninja who did trust their teammates, leading to a noticeable drop in survival rate. If it changes survival rate from even 99% to 97%, that would lead to a huge attrition difference over time.
Example: Most ninja lack super-divinatory capabilities. Faced with a glimpse of an enemy of unknown level, do you a) Hold back for fear of exposing your secrets to your teammates, or b) Unleash the most powerful attack you can feasibly muster?
Any team that adopts a 'temporary member' without full disclosure become markedly less effective than their composite ninja ranks would suggest, and the Mori and Nara would have noticed this. It seems much simpler and safer for even temporary team members to reveal their full-spectrum capabilities to each other upon the acceptance of any remotely dangerous mission, thus ensuring mutual reciprocal blackmail (if they even need to) without compromising their ability to actually win fights. Anyway, just my two cents.