The ultimate test would be a DNA link to the Gibson side but in the absence of that, James Alan Reekie's birth registration would be as you would expect, connected to Mary's first marriage:
REEKIE, JAMES ALAN - Mother's maiden name CULLEY
GRO Reference: 1904 S Quarter in NEWCASTLE-UPON-TYNE Volume 10B Page 39
From the other post linked above, Mary's first husband James didn't die until 1907?
Monica