Your observation is correct, and noting the angular relationship between lower and upper rock strata was an important step in the early history of modern geology. See this Wikipedia entry on James Hutton

The rocks of the inner gorge are the ancient metamorphic rocks. They are known as the Yavapai Series and are typically dated to around 1.7 GA (that's 1.7 billion years, AKA the Proterozoic). I got to know them very well while doing geologic mapping in Arizona. The metamorphic fabric (foliation) was developed in a nearly vertical orientation throughout the region; however, the original sediments and volcanics that were metamorphosed were deposited in horizontal layers. Those layers were folded into very tight folds that nearly match the vertical foliation.

That material was eroded down, and the later (upper) sedimentary deposits were laid down as horizontal layers on top of that "basement" rock. This "angular uncomformity" is proof alone for the enourmous age of the rocks that make up the Grand Canyon. (there is another angular uncomformity between the Proterozoic rocks and the upper sedimentary column, but I just wanted to present the general picture)