I have no doubt that Red Bull's comments are entirely based on their competitiveness. For a long time, the most important thing to perform well in f1 has been aerodynamics. Red Bull has had the best expertise for some time now, and their car has been known to be the best car aerodynamically. It is therefore in Red Bull's interest to eliminate other factors in order to benefit from having the best aerodynamics. With the Pirelli tyres, there is now another factor that massively influences the performance and here Red Bull is not best. Of course, aerodynamics is still important, and I suspect that the difference between the top teams and the back markers is mostly due to aerodynamics. But teams like Lotus and Ferrari are sufficiently close to Red Bull aerodynamically, so that their better tyre management is enough to perform better than Red Bull, at least on some tracks.
This actually reminds me of a quote from Enzo Ferrari: "Aerodynamics are for people who can't build engines." With the same motives, Red Bull could now say something quivalent, like: "Tyre management is for people who can't produce downforce."