Can I wear an overseas service bar for a 6 month deployment from a different branch if it meets the criteria stated in 670-1?

You can wear what you earned and got in your records. Refer the individual complaining to the AR.
That would be like saying someone who won the Navy MOH can't wear it if he joined the Army.

DOD and U.S. military, awards currently issued to service members
Order of precedence
Notes: Precedence of particular awards will vary slightly among the different branches of service. All awards and decorations may be awarded to any service member unless otherwise designated by name or notation.

PERSONAL DECORATIONS - COMBAT
Medal of Honor - Highest Military Award (all services) - Awarded for "gallantry and intrepidity at risk of life above and beyond the call of duty" (May be worn while in Civilian Clothing.)
SERVICE CROS MEDALS - Awarded for "extraordinary heroism"
Distinguished Service Cross (Army)
Navy Cross
Air Force Cross
Coast Guard Cross
DISTINGUISHED SERVICE MEDALS - Awarded for "distinguished service under hostile fire"
Defense Distinguished Service Medal
Homeland Security Distinguished Service Medal
Distinguished Service Medal (U.S. Army)
Navy Distinguished Service Medal
Air Force Distinguished Service Medal
Coast Guard Distinguished Service Medal
AWARDED FOR "GALLANTRY IN ACTION"
Silver Star
Awarded for "superior or exceptionally meritorious service"
Defense Superior Service Medal
Legion of Merit
Awarded for "heroism or extraordinary achievement in aerial flight"
Distinguished Flying Cross
Medals for non-combat heroism
Soldier's Medal (V for Valor may be awarded for a single or sequentially or concurrent acts of heroism.
Navy and Marine Corps Medal
Airman's Medal
Coast Guard Medal
Awarded for heroism in combat zone or meritorious service in a war zone
Bronze Star Medal
Awarded for wounds suffered in combatPH
Purple Heart

MERITORIOUS SERVICE AND AVIATION MEDALS (COMBAT or NON-COMBAT)
Defense Meritorious Service Medal
Meritorious Service Medal
Air Medal
Aerial Achievement Medal

COMMENDATION MEDALS (COMBAT or NON-COMBAT)
Joint Service Commendation Medal
Army Commendation Medal
Navy and Marine Corps Commendation Medal
Air Force Commendation Medal
Coast Guard Commendation Medal
Achievement medals
Joint Service Achievement Medal
Army Achievement Medal
Navy and Marine Corps Achievement Medal
Air Force Achievement Medal
Coast Guard Achievement Medal
Commandant's Letter of Commendation (not normally a Ribbon Award)
Combat Action awards
Navy Combat Action Ribbon
Coast Guard Combat Action Ribbon
Air Force Combat Action Medal
Also see: Army combat badges for special instructions, waiver may be required between services.

UNIT AWARDS (Normally worn on opposite side from Personal Awards) (COMBAT or NON-COMBAT)
Presidential Unit Citations
Army Presidential Unit Citation
Navy and Marine Corps Presidential Unit Citation
Air Force Presidential Unit Citation
Coast Guard Presidential Unit Citation
Joint Meritorious Unit Award
Army Valorous Unit Award
Navy Unit Commendation
Air Force Gallant Unit Citation
Coast Guard Unit Commendation
Meritorious Unit Commendations
Army Meritorious Unit Commendation
Navy Meritorious Unit Commendation
Air Force Meritorious Unit Award
Coast Guard Meritorious Unit Commendation
Army Superior Unit Award
Air Force Outstanding Unit Award
Coast Guard Meritorious Team Commendation
Efficiency Awards (non-combat)
Navy "E" Ribbon
Air Force Organizational Excellence Award
Coast Guard "E" Ribbon

SERVICE AWARDS
Prisoner of War Medal
Good conduct medals
Army Good Conduct Medal
Navy Good Conduct Medal
Air Force Good Conduct Medal
Marine Corps Good Conduct Medal
Coast Guard Good Conduct Medal
Combat Readiness Medal (Air Force)
Outstanding Airman of the Year Ribbon
Coast Guard Enlisted Person of the Year Ribbon
Air Force Recognition Ribbon
Reserve medals
Army Reserve Components Achievement Medal
Air Reserve Forces Meritorious Service Medal
Selected Marine Corps Reserve Medal
Coast Guard Reserve Good Conduct Medal
Armed Forces Reserve Medal
Expeditionary medals
Navy Expeditionary Medal
Marine Corps Expeditionary Medal
General service medals
National Defense Service Medal
Global War on Terrorism Service Medal
Korea Defense Service Medal
Armed Forces Service Medal
Humanitarian Service Medal
Outstanding Volunteer Service Medal
Special service medals
Antarctica Service Medal
Coast Guard Arctic Service Medal
Air and Space Campaign Medal
Nuclear Deterrence Operations Service Medal
Campaign and Expeditionary / Conflict Service Medals
Armed Forces Expeditionary Medal
Afghanistan Campaign Medal
Inherent Resolve Campaign Medal
Global War on Terrorism Expeditionary Medal
Service and training awards
Navy Sea Service Deployment Ribbon
Coast Guard Sea Service Ribbon
Army Sea Duty Ribbon
Naval Reserve Sea Service Ribbon
Air Force Expeditionary Service Ribbon
Navy Arctic Service Ribbon
Navy and Marine Corps Overseas Service Ribbon
Coast Guard Overseas Service Ribbon
Air Force Overseas Short Tour Service Ribbon
Air Force Overseas Long Tour Service Ribbon
Army Overseas Service Ribbon
Army Reserve Overseas Training Ribbon
Coast Guard Restricted Duty Ribbon
Coast Guard Special Operations Service Ribbon
Air Force Longevity Service Award
Recruiting service and Training service ribbons
Navy Recruiting Service Ribbon
Marine Corps Recruiting Ribbon
Coast Guard Recruiting Service Ribbon
Navy Recruit Training Service Ribbon
Marine Corps Drill Instructor Ribbon
Marine Corps Combat Instructor Ribbon
Air Force Special Duty Ribbon
Guard ribbons
Navy Ceremonial Guard Ribbon
Marine Corps Security Guard Ribbon
Professional development Ribbons
Army NCO Professional Development Ribbon
Air Force NCO PME Graduate Ribbon
Air Force Basic Military Training Honor Graduate Ribbon
Coast Guard Basic Training Honor Graduate Ribbon
Navy Basic Military Training Honor Graduate Ribbon
Army Service Ribbon
Air Force Training Ribbon

MARKSMANSHIP AWARDS (Not Transferable Between Services)
Air Force Small Arms Expert Marksmanship Ribbon
Rifle
Coast Guard Distinguished Marksman Award
Coast Guard Silver Rifle Excellence-in-Competition Award
Coast Guard Bronze Rifle Excellence-in-Competition Award
Navy Expert Rifleman Medal
Coast Guard Expert Rifleman Medal
Navy Rifle Marksmanship Ribbon with Sharpshooter Device
Coast Guard Rifle Marksmanship Ribbon with Sharpshooter Device
Navy Rifle Marksmanship Ribbon
Coast Guard Rifle Marksmanship Ribbon
Pistol
Coast Guard Distinguished Pistol Shot Award
Coast Guard Silver Pistol Excellence-in-Competition Award
Coast Guard Bronze Pistol Excellence-in-Competition Award
Navy Expert Pistol Shot Medal
Coast Guard Expert Pistol Shot Medal
Navy Pistol Marksmanship Ribbon with Sharpshooter Device
Coast Guard Pistol Marksmanship Ribbon with Sharpshooter Device
Navy Pistol Marksmanship Ribbon
Coast Guard Pistol Marksmanship Ribbon

Did you get credit for a full tour?