For the purpose of understanding the statement from Coyle, you need to realize that "travel", to them, is the cost of getting you to/from the hotel. Not the cost of the hotel stay.
The line about meals being on your own is just a clarification point for the posting, since most Coyle hotels offer some meals. You never have food reimbursed unless it's part of the assignments anyway, but that lets you know the assignment requirements will be lighter then normal.
If you are at a higher membership tier with the rewards program for that particular hotel chain, you will receive a free breakfast each morning, however. No reporting required....and it's been asked elsewhere, but I kept my points from the test visit for this client.