[Questioner asked a followup question, saying that s/he was aware of someone named Ray Kelly who was an 18 year old marine stationed in the UK in 1955, and was trying to find out if NYC police commissioner Kelly was that Ray Kelly].
Biographical data about Kelly in another New York Times article ( August 4, 1992, Tuesday, Late Edition - Final. SECTION: Section B; Page 2; Column 1; Metropolitan Desk. BROWN'S RESIGNATION; Interim Leader Has a Reputation as a Problem-Solver. By MICHEL MARRIOTT). says that he received his undergraduate degree from Manhattan College in 1963. Among other degrees and dates included in that article.
That article also says: "Having considered a military career, he became interested in police work soon after joining the Police Cadet Program at Manhattan College. Upon graduation, Mr. Kelly, who was born and raised on the Upper West Side, became a city police officer at age 21.
"Almost immediately, however, he took a leave from the department to serve three years in the Marine Corps, including a year in Vietnam."
So, while Kelly was in the marines, all of this information does seem inconsistent with him being in in the marines in 1955 at an age of 18. Along with the 1941 birthdate I found in the other article. Unless, as you say, for some reason this information in New York Times articles can't be trusted; it's certainly possible that the info in those articles is false (although one would hope that the NYT writers would do some basic fact checking of at least some of the biographical info given by Kelly, we can't verify that for sure), but I'm not sure where else to go.
There are many other people named Ray Kelly, I'm afraid. The "Biographical and Geneological Master Index", which largely indexes entries from the various "Who's Who..." books, lists a couple dozen Ray or Raymond Kelly's--and those are just the ones who have done something notable enough to be listed in a "Who's Who" book.
Actual military records might be one way to figure out exactly what the NYC commissioner Kelly dates of service were. Here is some information on requesting military records, but it looks like specific personal information that you do not have is required to request all military records (and permission of the person involved is required for some):
The website of the National Archives and Records Administration has information on obtaining military personnel records at http://www.archives.gov/facilities/mo/st_louis/military_personnel_records.html
Limited information is available to members of the general public via these requests according to the FOIA, and is outlined at http://www.archives.gov/facilities/mo/st_louis/military_personnel_records/foia_info.html#mprfoia
Information for the general public seeking to obtain such records is at http://www.archives.gov/facilities/mo/st_louis/military_personnel_records/general_public.html