Reimbursed expenses as a sole contractor

I work as a sole contractor doing work that involves traveling for a client. They reimbursed me for various travel expenses that were directly related to a contract I fulfilled for them: plane ticket, per diem for meals and cab fares. I understand that as these expenses were reimbursed, I cannot declare them as business expenses. However, they still seem to count towards my taxable revenue total. How does this make sense, given that this is basically money my client is spending? Is the idea that as a sole contractor, I am basically generating revenue out of charging the client for expenses entailed by the job they contracted me for?