I'm sure that was true - for members of the Regular army. But since by far the majority of soldiers during the war were volunteers serving in state regiments that likely varied widely, particularly in 1861. True, very soon the volunteers were wearing uniforms, etc. largely provided by the Federal government to the states for issue; nevertheless, the issue of the uniforms was completed at state level. Another anomaly was the direct purchase of uniforms by the states, again most common in 1861. Here's an example of this from my collection I have frequently posted before in the forums, but which illustrates pretty well the situation as it existed at the beginning of the war:
View attachment 412723
I purchased this image precisely because it illustrated many such anomalies, especially in the totally non-regulation FIVE-button sack/frocks they're wearing! I sent a copy of this ambrotype to Michael Macafee, then curator of the U.S. Army museum at West Point and a specialist in uniforms of the Civil War. According to him, these men are members of Company E of the 13th Wisconsin Vol. Inf. ca. 1861, evident from the letter E's on their forage caps (worn against regulations) and brass 13's on their stand-up collars, needless to say again totally against regulations. He said these unusual uniforms were delivered to the state and issued to several regiments including the 13th. (In case you or anyone else wonders what's going on with this brass, both subjects have turned the E's upside down and the man on our right has done the same with the 3 on his collar in order to make them look "right" for the camera! they're also holding their so-called
Dresden rifles in their LEFT hands to make it appear that they're holding them correctly in their right hands.) Other anomalies include the wearing of boots instead of brogans and cartridge boxes on their waist belts instead on over-the-shoulder straps.