Why is NOAA & PHS considered part of the Uniformed Services?

For NOAA - In short so they wouldn't get killed for being spies -
While NOAA was born in 1970 is origins go way back as a uniformed service. The NOAA Commissioned Officer Corps traces its roots to the United States Coast and Geodetic Survey. The Coast and Geodetic Survey's predecessor, the United States Survey of the Coast – renamed the United States Coast Survey in 1836 – was founded in 1807 under President Thomas Jefferson. Until the American Civil War, the Coast Survey was manned by civilian personnel working with United States Army and United States Navy officers. During the Civil War (1861–1865), Army officers were withdrawn from Coast Survey duty, never to return, while all but two Navy officers also were withdrawn from Coast Survey service for the duration of the war. Since most men of the Survey had Union sympathies, most stayed on with the Survey rather than resigning to serve the Confederate States of America; their work shifted in emphasis to support of the U.S. Navy and Union Army, and these Coast Surveyors are the professional ancestors of today's NOAA Corps. Those Coast Surveyors supporting the Union Army were given assimilated military rank while attached to a specific command, but those supporting the U.S. Navy operated as civilians and ran the risk of being executed as spies if captured by the Confederates while working in support of Union forces. After the war, U.S. Navy officers returned to duty with the Coast Survey, which was given authority over geodetic activities in the interior of the United States in 1871 and accordingly was renamed the United States Coast and Geodetic Survey in 1878.

For PHS - The PHS Commissioned Corps traces its beginnings back to the U.S. Marine Hospital Service protecting against the spread of disease from sailors returning from foreign ports and maintaining the health of immigrants entering the country. Under John Adam in 1798 the "Act for Relief and Disabled Seamen" was enacted and slowly became a network of coastal Marine hospitals. Later a centralized HQ was created in DC under the supervising surgeon later titled the Surgeon General.

Much like Army Corp of Engineers these uniformed services where more or less branches of the Army and Navy that split off like the Air Force to form their own uniformed service. So yes while not under the DoD command they do receive benefit.

Yes they do. As an example, the Surgeon General is actually an Admiral in the (US)PHS.

Think of them like the Chaplain Corps. "Uniformed" but not "Armed."

Officers have specific Powers, as opposed to (Special) Agents, hence the difference. Although the Uniformed Services administratively, & operationally fall under the Executive Branch, we answer to the Constitution ("the appointment of the officers" Art 1, Sect 8) . Special Agents generally answer to the Executive Branch, as their authority comes from the Cabinet Level, as opposed to the Constitution itself.

Perhaps this will help SFC(P) (Join to see):

http://vip-promis.blogspot.com/2015/04/uniformed-services-of-united-states.html