I believe in some cases European culture can directly affect American art, but truthfully this very much depends on the artist. Artists come in all shapes, sizes, and economic backgrounds. Some artist know little of art history and others have studied it. All of these experiences or lack of experiences determines what an artist may be influenced by.
Yes, European culture directly affects American art. Many American artists study abroad and spend time in Europe. Cultural capitols like New York often host European artists. American culture has many roots in European culture - it began when colonists from all over Europe settled in North America - the colonies had Dutch, English, French, German, and Spanish settlers. That cultural connection continues today.
People in the US have the same culture as Europe - Western culture is generally very similar, and the differences within it are far different than the differences between Western and Non-Western culture. European culture, therefore, has an influence on American art and has had an influence since its inception.
Yes, European culture directly affects American art, because people in America often take their cures from Europe. This doesn't make much sense, because their financial structure is a mess, and we broke away from them in the 1700s for a reason. But artists especially tend to think that if something is European it is better.
There was a time up until the 1950s or so when American are was heavily influenced by Europe, because Europe was the epicenter of all things artistic, especially in the 19th and early 20th century. Another reason why American art were heavily influenced by European art was that the United States was such a young nation that it had yet to develop its own style and would look to overseas for direction. By the 1950s or so, however, Americans started developing their own homegrown style, and Europe began to decline as a major artistic force. Because of this, American art is no longer directly impacted by European art. If anything, it's now the other way around, with trends in American art directly impacting Europe.