This contractor will only have travel expenses reimbursed and no service income. I am confused as to the company is required to give a 1099-misc at the end of the year for his travel expenses.

Because the contractor will likely deduct the travel expenses on his Schedule C and conveniently "forget" to report the reimbursement for those expenses.

That is why the IRS requires that you issue him the Form 1099-MISC, to make him account for the reimbursement.