The above is the entire statement about the rotunda state funeral from Wikipedia. Notice their quotes about the title, implying that it is not the main event. I do not have their source.
Part of the problem here is relying on sources like Wikipedia, the Washington Post, and unfortunately, even the White House web page. All of these sources have implied that the ceremony at the Capitol is The State Funeral . However, if you go to the Military District of Washington web page on the funeral, they make it clear that all of the ceremonies, including the portions in California and Michigan are all part of the State Funeral. That portion of the State Funeral held at the Capitol is referred to as the Lying in State portion.
(see MDW Schedule )
I point this out because it has become a pet peeve with me. No one cares about getting it right anymore. Certainly not the media, and increasingly, government officials are just as bad. They play fast and loose with people and events that have titles embodied in law and custom. Newpapers and government offices used to have people who were educated in such formalities and who checked to make sure that the terms were properly used. We don't do that anymore - make it up as we go, do whatever feels good. Sloppy, in my opinion.
In my part of the country, when a funeral procession goes by, no matter who it is, people pull over and get out of their vehicles .