Yes it is partly a tongue in cheek phrase, but the JAZZBROS tag also represents my philosophy of how I think a band should function.  Time for a little story time...

Although I was born and raised in Austin, Texas, at age 17 I moved to New Jersey to attend college.  This wasn't just anywhere in New Jersey, but North Jersey.  The Sopranos takes place 15 minutes from the college I went to, and MTV's "Jersey Shore" (which came out the same year I moved north) had at least one member of the cast attending William Paterson.  Within the jazz department there were people from the Pacific Northwest, Baltimore, Scotland, Japan, and even other people from Texas.  On the other side of the spectrum, the prestigious academics of the rest of the University attracted people from as far away as Bayonne, Leonia, Montclair, and even in some rare cases, south Jersey.  Many of the people I met while I was at WPU had absorbed the "Bro Culture" of New Jersey into their life in one way or another.

Sometimes, this manifested itself in the practice room.  Each ensemble rehearsed twice a week; once with a "coach" from WPU's faculty, and once without.  In the student run rehearsals, there was usually a laid back atmosphere with some lighthearted insults, and some of what might be colloquially known as "ball busting."  These were some of the most relaxed rehearsal situations I'd be in for the next few years up until I started booking gigs for myself as a leader.  In the rehearsals at WPU, there was hardly ever an awkward silence around a musical issue that wasn't being acknowledged.  There was little to no miscommunication over what people wanted out of each other in the ensemble.  Nobody was afraid to express their opinion on the music, and as a result, we dealt efficiently with musical issues and were making music on the highest level we could based on our individual talents at the time.  The "Bro Culture" of ball busting let people feel free to speak their minds without worrying about bruised egos.

When I moved to NYC, I noticed that the general culture was a little different.  At many public and private jam sessions, there was almost none of the chumminess I had become accustomed to in New Jersey.  Sometimes people would feel compelled to carefully word their complements to avoid seeming unintentionally patronizing.  On multiple occasions in certain bands I worked in, I would see tension build up over the course of several rehearsals while none of it was discussed.  Two people having a small difference in opinion (could be musical aesthetics, preferences on who to hire for a certain chair, how to deal with money, or any one of a number of other issues) would go undiscussed and slowly metastasize into serious problems that would blow up and sometimes result in one or multiple people quitting the band.

As a result, when I started leading my own bands, I started using the term JAZZBROS to describe myself and the people I chose to play with.  I would purposely cultivate an atmosphere where people could give their (sometimes unpopular) opinions without dealing with any serious blowback.  If you're a musician reading this, think of the bands you're in where you feel comfortable issuing a light-hearted insult to another member of the band.  In my experience, these are the groups that can have open discussions about music -- nobody feels like they will be ostracized for an opinion.

Four years later, I still stick to this philosophy, and as an added benefit, the constructive criticism I receive from my JAZZBROS opens my ears to gaps in my playing I may not otherwise notice.

TL;DR -- JAZZBROS is about really being friends with the musicians you work with.  Just like you don't stop being friends with someone over a difference of opinion, your musical opinions won't alienate you from your JAZZBROS.  In this context, a "Bro" is someone who you can talk with honestly and directly because you aren't worried about accidentally offending them.