Reimbursing contrators is a dicey situation legally. If you do it, then you are paying the expense and as such you need to have the original expense receipt for your records.
The vendors invoice to you his customer is your bill by the way
Typically what you pay to a contractor is his income, and he has his expenses which reduce that income. What you pay a contractor is also reportable on the 1099 at the end of the year if paid by check or cash and over $600 annually.