That's not Universals fault that it just an example of how stupid the public can be sometimes. As far as park confusion is concerned, all the promotion in the world doesn't make the public any smarter. I have heard so many people looking for or commenting on things that the saw at Disney that were either in Universal or Sea World or Bush Gardens.
Disney didn't help by having Disney/MGM studios. Very few people are savvy about movie studios. The may like a movie but you never hear them say... That MGM movie was great. They don't really connect a movie with a specific studio. Having the Disney/MGM tended to confuse people that weren't fully versed on that stuff so when they heard Universal mentioned they just assumed it was in Disney. Not really lack of branding just lack of working knowledge. I suspect most of us fall into that category especially if we don't spend a lot of time in Theme Parks.