Everyone making nuBSG categorically stated that in their universe, there were no aliens. RDM said it, EJO said it (and threatened to walk off the job if aliens were ever introduced), so I'd count that as canon.
I've never heard anyone say that aliens don't exist, period. As far as I know, it was only implied that they wouldn't be included due to the show's nature as well as Olmos' feelings on the matter. It's entirely possible for the viewer to speculate that they might exist, just that we don't and won't see them. We don't see aliens or ninjas on
Seinfeld. That doesn't mean that they don't exist, it just means that we don't see them because they're not part of what the show is trying to do.
Since No Aliens was a rule in the NuBSG Universe, it's natural when someone says "In the BSG Style", to presume that one aspect of that means without Aliens. If that wasn't intention, that's fine, but, it should be stated, that "No Aliens" aspect, wasn't supposed to be considered, and exactly what "NuBSG Style" does mean, otherwise, other aspects of the show, may be wrongly assumed to be intended, IMHO, of course
To me, "BSG-style" simply means naturalistic (and maybe a bit over-the-top) drama with realistic effects and production values. In other words, Sci fi that looks like it can happen in the real world. It's not as specific as "no aliens".
Stargate Universe,
The Walking Dead and I believe
Falling Skies use that style and they have aliens, with monsters in
The Walking Dead's case. I think BSG-style can include anything, so long as the naturalism I mentioned remains at the core. We're just talking TV shows. Lots of movies have already done this, like the Alien and Terminator franchises as well as one-offs like
Solaris,
The Abyss,
Sphere, etc. I see all those as BSG-style.