Yes there is a higher form of Art, namely Fine Art. There is even a degree course for it. You either go the graphic Arts route which is highly commercial and making art as a product. Fine Art or "High Art" is making Artwork for the sake of Art itself. The Term Fine comes from metals that have been purified and refined with no impurities. People that think everything is art don't know the true meaning of Art. Art with a capital A, Art that has a deeper meaning than a superficial one. Yes there is such a thing as High Art. It is art that is not created to catered to commercial value but Art that is created from the Artist trying to capture a sense of reality in his/her own view and share it with the world. Not everything is art, but there is a lot of art out there; yet not everything is Fine Art or "High Art". The only Difference between Graphics Designers and Fine Artists and High Art is Philosophy.
I would argue that there is a thing such as high art, but it only exists as a category that some people prefer to use. Whether or not a piece of art fits that constraint is up to the viewer, as there are no predefined parameters that define aesthetic beauty.
Art has value because people give it value. Because visual art does not have any significant meaning outside the realm of human perception, a piece of art is defined as "good" or "high" because of the impact it has on those who view it. A Pollock or Basquiat may be seen as self-indulgent garbage to some, but to others, it is profoundly deep and meaningful. While there are rules to making art, it is all completely subjective in the grand scheme of things. Therefore, I do not believe that there is such a thing as 'high art'.
Art is art, and while there may exist expensive art, art that is not for sale, inexpensive art, and art for which varying degrees of attention and effort went into making, I don't believe that anyone has the right to term art "high" or otherwise. Art is creation, and is subjective.
I don't believe there is such a thing as "high art." What is "art" to one person is obnoxious trash to another; that is especially true in the case of modern art and other forms of expression that some people simply want no part of. Trying to differentiate any particular form as "higher" than another just seems like snobbery.