The Standard deduction allows people with a low yearly income to not have to submit a tax return, correct?
As pointed out by others in this thread, that's not always true. Having income below the standard deduction is only a single criteria of many. It can depend on other things such as source of that income, weather you qualify as a dependent or not, one's filing status, what credits if any, you may qualify for regardless of income, etc.
Additionally, even if one's income is below the standard deduction, if taxes were withheld from one's pay they may want to file a tax return to get those withheld taxes refunded to them.
Also, if your income "BEFORE" deductions is over the standard deduction, then a tax return would be required. But again, the "standard deduction" is not the only factor here.
