Yes, it is safe to assume that reporting more income should not be an issue. As a matter of fact, it is quite normal that not all gross receipts earned be reported on Form 1099.
Remember, there are other kinds of income, like tips or cash income, that may be taxable, but don't require Form 1099. In those cases, it's your responsibility to track and accurately report those types of income. For additional information on how IRS verifies income, see this link: How The IRS Verifies Income
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