I don't think anyone was suggesting you were a tax dodger. Keep in mind, other people than the OP read these threads. I gave a comprehensive reply to avoid someone coming here and thinking "then I don't have to report it" if we were to just tell you, "yes" or "no" without explanations.
As wales said, both approaches are okay as long as the net result is a correct computation of the net income. I suggested my approach (which is the same as Flash's) because it eliminates the need to do different accounting based on what the MSC will do (include or not include the reimbursements as income on the 1099). If you count every penny as "income" and then just deduct all your expenses, you will get the same result as if you had extra columns in your spreadsheet for "reimbursements on 1099" and "reimbursements not on 1099". For probably every one of us, our total income for the year is going to be more than the sum of our 1099's because we won't get at least $600 from every company. If your 1099's total $2000 and your reported total income is $3000, the IRS is happy. If your 1099's total $3000 including reimbursements and you only put $2500 on the return because you're subtracting out the reimbursements from the income figure instead of putting them as an expense, you will get a letter from the IRS asking for tax on the $500 difference. Then you have to write them a letter saying, "Part of the 1099 was for reimbursements that totaled $500." That could conceivably result in a request for proof and details.
You avoid all that by just keeping everything you got paid in one total called "income" and put all the money you laid out in another total called "returns and allowances" or "misc expenses."
(Keep in mind, you can always get tagged for a random audit and will have to provide details of everything if that happens.)
You should also keep in mind that you report income in the year you receive the money, not the year you earn it, unless you are doing accrual accounting (most taxpayers don't). This is especially important for mystery shoppers because at the end of the year, you may not know for a couple of months if you will or won't get paid for something but you might want to get your tax return done before that. You should deduct your expenses in the year you paid them, and claim the income and reimbursement in the year you receive the check. Otherwise if you end up not getting paid for something, you will have already deducted your out of pocket costs and the date on the receipt will match the year of the tax return.
I know that's a lot more than you asked, but tax questions are rarely "yes or no" questions. There's more gray area in the tax code than you'll find on a whole herd of elephants.
Time to build a bigger bridge.