The birth certificate you obtained from 1856 is certainly a possible keeper. As I mentioned, the birth dates on the census were often wrong, and Murdo put July 1855 on the 1900 census.
Then you have the Burke Funeral Home record from the Saratoga GenWeb website:
Name: Murdock Urquhart Age: 77y, 3m, 29d Born: Glasgow, Scotland Birth date: July 4, 1852 Death date: Nov. 3, 1829 Cemetery: Greenridge Residence: 106 White Street Occupation: Mason for D&H Railroad Company Father: (blank) Father's birthplace: (blank) Mother: (blank) Morther's birthplace: (blank) Spouse: Helen W. Harvey
Perhaps a New York death certificate would provide the parents names, even though the funeral home record does not. And, can you rely on the funeral home record having the correct birth date and birth place???