Text to support assertion a BDU hat is required.

[ol'fido]

Are you assuming that the uniform is just the pants and top? To me the uniform is the pants, top, hat, etc. If that is the case, then a separate cite about the hat would be redundant.

[brasda91]

CAPM 39-1 table 2-3 line 6

All senior members do not wear any type of insignia on the cap.

^ This is not correct.  Per ICL dated 25 Jan 2008:

g. Embroidered Grade Insignia on BDU cap for senior members. Effective
20 November 2006, the Air Force authorized the wear of the ultramarine blue
embroidered grade insignia centered on the BDU hat by senior member officers. The
grade insignia may be worn immediately and a mandatory wear date of 1 May 2007 was
established.