In the Wikipedia article on "Love Me Tender" it is written that
The song is credited to Elvis Presley and Vera Matson due to royalty issues, but the lyric was written by Ken Darby (Matson's husband). He also arranged the Civil War tune, which was in the public domain. When asked why he credited his wife as co-songwriter along with Presley, Darby responded, "Because she didn't write it either." Darby also wrote the other three songs in Love Me Tender. It has been said that Elvis didn't like any of these songs, except the title tune. Elvis Presley received co-songwriting credit because he was involved in the creative process in producing this song. As with nearly all Elvis RCA recordings, Elvis took control in the studio despite not being credited as producer. Elvis would regularly change arrangements and lyrics to the point that the original song was barely recognizable. This, arguably, justified the co-songwriting credit in this song. Elvis received co–songwriting credit because he wanted it. Being a co–writer was simply a way to increase his income. Darby's statement tells what he thinks of the argument that whatever Elvis did deserved co–credit—"She didn't write it 'either'."
Elvis is listed as a co–writer on most or almost all of the new songs he recorded.
The Truth
It is true that Vera Matson did not deserve credit for "Love Me Tender" but Elvis Presley didn't deserve credit either. Neither of them wrote the words or music.
Naturally Elvis was involved in the "creative process" during the recording but according to Darby himself, Elvis listened to what Darby suggested about having a simple vocal delivery and followed that suggestion. Elvis was very respectful on his first film because he had high hopes for his future movie career.
What is also not correct is the sentence:
"Elvis received co-songwriting credit because he wanted it."
It was actually Colonel (an honorary title) Tom Parker, his shrewd and often ruthless manager, who made sure that Elvis received co-writer credit on his early RCA records, including "Love Me Tender." Also for the biggest Elvis hit of that era, "Don't Be Cruel," written entirely by songwriter Otis Blackwell. This shameful practice denied the full royalties to the songwriters who wrote the song. To his credit, Elvis never said he had co-written any of these songs. It was Parker who insisted on songwriting credit to gain more attention and money for "his boy" and to fill Parker's pockets too.
The Songwriter
As stated above, the songwriter who wrote "Love Me Tender" was Ken Darby (1909-1992).
This rare photo shows Ken Darby working with Elvis Presley on the songs for Love Me Tender... 
[Photo courtesy of Films in Review, June-July 1969]
Ken Darby began his professional music career as a member of The King's Men. They were featured in early films including B-westerns like The Renegade Trail (1939), with Hopalong Cassidy.
Later on, he formed the Ken Darby Singers and they frequently performed with Bing Crosby on radio and records. These same singers are featured on Bing's multi-million-selling holiday record classic: "White Christmas."
In the early 1950s, Darby went to work at 20th Century Fox as as an arranger, songwriter and choral conductor.
While working there he received three Oscars for his adaptations of these Hollywood musicals: The King and I (with Alfred Newman, 1956)
Porgy and Bess (with Andre Previn, 1959)
Camelot (with Alfred Newman, 1967)
He also received a Grammy Award for his work on Porgy and Bess in 1959.
He wrote all four songs sung by Elvis in Love Me Tender. Darby based the title song on the Civil War era ballad tune,"Aura Lee (or Lea), words by W.W. Fosdick and music by George R. Poulton.
Darby arranged the 1861 tune and added his own words.
So he should be credited as the ONLY songwriter for "Love Me Tender."
Besides the title song there were three other songs written by Darby: "We're Gonna Move," "Poor Boy," and "Let Me."
It has been said that Elvis didn't like these songs except for the title tune. Yet Elvis managed to put his stamp on all four songs, maybe because he had deep roots in country music and the simple tunes were well suited to his voice. Darby wrote songs that demonstrated a different side of Elvis, a more polished singer. Elvis wasn't pleased that his usual backup combo of Scotty Moore, Bill Black and D.J. Fontana were not used on the soundtrack. Instead, Ken Darby used studio musicians.
When Darby was asked why his wife's maiden name (Vera Matson) was on "Love Me Tender" as co-writer, he replied: "Well, she didn't write it either!" Actually, he said he wasn't interested in being credited for such a medicore movie starring the young rock n' roll sensation. He probably thought Elvis wouldn't last as a film or recording star. How wrong he was!
Ken Darby was happy with the royalties his wife received as co-writer of "Love Me Tender."
He said the huge royalties helped to pay for their family boat!