Everything can be said one way, or the other. Hitting someone with full blame with no diplomacy in between will get people to be defensive. I don't get why "I'll stop reporting" is a childish thing to do - a mod just asked him to do that. They provided no easy way to differentiate between "misinformation worthy" and "not". Hell, they even had two mods say the exact opposite thing and then heard "do what we both tell you". The way it starts with a screenshot, first conversation they ever had, no "hey wanted to talk about something I've been seeing recently". Like, read the exchange and assume BB is pissed / annoyed, and Squid is neutral / doesn't know at the start, and becomes pissed / annoyed later. Like the "you should know better" message - are you there to stop the reports, or are you there to tell off / antagonize the user? "happening for months" is also a huge "nono".
This is something that corporations teach every manager / team leader in the company. To not use absolutes, to not embelish, to use language that refrains from personal observations and instead focus on facts and truths. "you are always late" when someone had to drop off kids twice this week because their spouse was sick. "You never do what I ask you" when someone has done 19 things you asked them, and forgot the 20th - which to you happens to be the "important" thing, but you haven't communicated that priority to them. All of these piss people off and diminish their contribution / their effort or their circumstances.
They absolutely should have talked to the other mod. If this indeed has been happening for months and was "annoying" enough to warrant a confrontation, it needs to be talked about among the modteam. There are millions of people out there in the world, each with their own character, their own beliefs and behaviors. One person would get annoyed, the other welcomes it. Ultimately it needs to be agreed as to what needs to be done - this isn't some huge violation that's blatantly obvious as being "bad and requiring corrective actions". And if it is - it requires mods to talk about it first. And if it isn't - it can be met with a shoulder shrug and two button presses that probably say something to the line of "ignore report".