"Decorated Veteran", technically speaking, is anyone who received a "decoration", using AR 670-1 as a guide.
Per AR 670-1 (2005), 29–6. Order of precedence within categories of medals (in this case, focusing on "decorations"):
U.S. military decorations. A decoration is an award given to an individual as a distinctively designed mark of honor denoting heroism, or meritorious or outstanding service or achievement. U.S. military decorations authorized for wear on Army uniforms are listed below in order of precedence.
(1) Medal of Honor (Army, Navy, Air Force).
(2) Distinguished Service Cross.
(3) Navy Cross.
(4) Air Force Cross.
(5) Defense Distinguished Service Medal.
(6) Distinguished Service Medal (Army, Navy, Air Force, Coast Guard).
(7) Silver Star.
(8) Defense Superior Service Medal.
(9) Legion of Merit.
(10) Distinguished Flying Cross.
(11) Soldier’s Medal.
(12) Navy and Marine Corps Medal.
(13) Airman’s Medal.
(14) Coast Guard Medal.
(15) Bronze Star Medal.
(16) Purple Heart.
(17) Defense Meritorious Service Medal.
(18) Meritorious Service Medal.
(19) Air Medal.
(20) Aerial Achievement Medal
(21) Joint Service Commendation Medal.
(22) Army Commendation Medal.
(23) Navy Commendation Medal.
(24) Air Force Commendation Medal.
(25) Coast Guard Commendation Medal.
(26) Joint Service Achievement Medal.
(27) Army Achievement Medal.
(28) Navy Achievement Medal.
(29) Air Force Achievement Medal.
(30) Coast Guard Achievement Medal.
(31) Combat Action Ribbon.
c. U.S. non-military decorations. U.S. non-military decorations authorized for wear on Army uniforms are listed below in their order of precedence. Personnel will wear other U.S. non-military (Federal agency) decorations based upon date of receipt. If more than one decoration is awarded by the same agency, the decorations are worn in the order of precedence, as established by the awarding agency. Personnel will not wear U.S. non-military decorations that duplicate recognition for service or an act for which a military decoration has already been awarded. Awards given by a jurisdiction inferior to the Federal Government are not authorized for wear on the Army uniform, except as specified
in paragraph j, below.
(1) Presidential Medal of Freedom.
(2) Presidential Citizen’s Medal.
(3) President’s Award for Distinguished Federal Civilian Service Award.
(4) Department of Defense Distinguished Civilian Service Award.
(5) Secretary of Defense Medal for the Defense of Freedom.
(6) Secretary of Defense Meritorious Civilian Service Award.
(7) Office of the Secretary of Defense Exceptional Civilian Service Award.
(8) Surgeon General’s Exemplary Service Medal.
(9) NASA Space Flight Medal.
(10) Public Health Service Commendation Medal.
(11) Public Health Service Achievement Medal.
(12) Department of State Superior Honor Award.
(13) Decoration for Exceptional Civilian Service.
(14) Meritorious Civilian Service Award.
(15) Superior Civilian Service Award.
(16) Commander’s Award for Civilian Service.
(17) Achievement Medal for Civilian Service.
g. Foreign military decorations. Personnel who are specifically authorized by law to accept decorations from foreign governments may wear them in the order of their receipt after all U.S. decorations, the Good Conduct Medal, campaign and service medals, and service and training ribbons. (See chap 9, AR 600–8–22, for application procedures to request
authorization to accept and wear foreign decorations.) Personnel may not wear any foreign decorations on the uniform unless at least one U.S. decoration or service medal is worn at the same time. Personnel will not wear foreign awards
that do not conform to the standard U.S. size ribbon bar or medal.
h. Foreign unit awards. The following foreign unit awards, listed in their order of precedence, are authorized for wear on the Army uniform, when at least one U.S. decoration, service medal, or ribbon is worn at the same time.
(1) Philippine Republic Presidential Unit Citation.
(2) Republic of Korea Presidential Unit Citation.
(3) Vietnam Presidential Unit Citation.
(4) Republic of Vietnam Gallantry Cross Unit Citation.
(5) Republic of Vietnam Civil Actions Unit Citation.
(6) Fourrageres (no order of precedence).
(a) French Fourragere.
(b) Belgian Fourragere.
(c) Netherlands Orange Lanyard.
Now, of course there is a difference between "highly decorated" and "decorated" (using the order of preference as a guide). Additionally, "Decorated" can be 1 or more decorations, as well as more than one not so high decoration (two AAMs, or an AAM and an ARCOM).
Just my take, but using AR 670-1 is one way to look at it and offers a subjective look.
If a soldier has an AAM, then technically, he or she, "clinically speaking", using the "book" as a guide, is a "decorated veteran".