Per an email from the Administrative Director of
River Bend Cemetery Co. on 3/26/2019 he said:
James and Mary are indeed buried here as well in Section 65, Lot 2873, Graves 1F & 2F respectively. There are also Grace and Margaret Brindle buried on the rear side of this lot.

I have found the following records for James -

James Hatton Langston Brindle
Birth
27 May 1878 • Bolton, Lancashire, England
England & Wales, Civil Registration Birth Index, 1837-1915
Death
Sep 1971 • Westerly, Washington, Rhode Island, USA
-U.S., Social Security Death Index, 1935-2014 -
Name: James Brindle
Last Residence: 02891 Westerly, Washington, Rhode Island, USA
Born: 27 May 1878
Died: Sep 1971
State (Year) SSN issued: Massachusetts (Before 1951)

-Son Richard’s U.S., Social Security Applications and Claims Index, 1936-2007 -
Name: Richard Schofield Brindle
[Richard S Brindle]
Gender: Male
Race: White
Birth Date: 12 Nov 1922
Birth Place: Westerly, Washington, Rhode Island
Death Date: 13 Feb 1996
Father: James H Brindle
Mother: Mary Schofield

-U.S., World War I Draft Registration Cards, 1917-1918 – filled his card out on 12 Sep 1918, it shows the birth date of 27 May 1878 in England, gives his wife’s name as Mary Ann Ellen Brindle.
-U.S., World War II Draft Registration Cards, 1942

-1881 England Census
-1891 England Census
-1910 United States Federal Census of New Bedford, Bristol, Mass on Apr 28 – James age 31, Mary age 32, James H L Jr age 3, Grace I age 2, Roger age 3 mo.
-1920 United States Federal Census Westerly, Washington, RI on Jan 8 – James H L age 41, Mary A E age 42, James H Jr age 13, Grace I age 11, Roger C age 9, Margaret A age 8, Elsie J age 5
-1925 Rhode Island State Census in Westerly, Washington, RI – James age 46, Mary A E age 46, James H Jr age 18, Grace I age 17, Roger C age 15, Margaret A age 13, Elsie J age 11, Helen L age 4, Richard S age 2
-1930 United States Federal Census of Westerly, Washington, RI – James age 51, Mary A age 52, James H Jr age 23, Roger C age 20, Margaret A age 18, Elsie J age 16, Helen L age 9, Richard S age 8
-1935 Rhode Island, State Censuses
-1940 United States Federal Census – James age 61 was working in Lawrence, Essex, MA at the time of the census, while back in Westerly RI was Mary age 62, Roger C age 30, Margaret age 28, Helen age 19, Richard age 17.

-England & Wales, Civil Registration Marriage Index, 1837-1915
-England, Select Marriages, 1538–1973

-New York, Passenger Lists, 1820-1957
-U.S. City Directories, 1821-1989
-UK, Incoming Passenger Lists, 1878-1960
-UK, Outward Passenger Lists, 1890-1960