The Mississippi Confederate Grave Registry is know to contain many errors. I would say if the name and dates match the service is wrong. You might try to run down an obit from a local newspaper.

I found this on the LDS site, is this your John?

John H MC MATH (AFN: 4QBQ-N5) Pedigree
Sex: M Family

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Event(s):
Birth: 19 Jun 1826
, Tuscaloosa, Al
Death: 1874
, Carroll, Ms
Burial:
Providence/cem, Grenada, Ms

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Parents:
Father: Zedekiah MC MATH (AFN: 4QBQ-98) Family
Mother: Susan (Sookey) EDMONDSON (AFN: 4QBQ-BF)

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Marriage(s):
Spouse: Mary E (AFN: 230K-D0N) Family
Marriage: Abt 1840
, , Mississippi