The request for your parent's income comes from Form 8615, Tax for Certain Children Who Have Unearned Income.
I typically see this form appear as I'm doing my daughter's taxes and start to enter data from stock transactions. In other words, your earned income is your's. But if you are a dependent, or 'can be,' the flow avoids the potentially lucrative results from gifting children appreciated stock, and have them take the gain at their lower, potentially zero cap gain rate.
I suggest you grab a coffee and thumb through Pub 929 Tax Rules for Children and Dependents to understand this better.
From page 14 of the linked doc -
Parent's return information not available. If a child
can’t get the required information about his or her parent's
tax return, the child (or the child's legal representative)
can request the necessary information from the Internal
Revenue Service (IRS).
How to request. After the end of the tax year, send a
signed, written request for the information to the Internal
Revenue Service Center where the parent's return will be
filed. (The IRS can’t process a request received before
the end of the tax year.)
It also suggests that you file for an extension for the due date of your return. Include payment for the tax you expect to pay, say by plugging in $200K for parent income as an estimate.
My parents' accountant tells them I do not need it.
Well, a piece of software told you that you do, and 3 people on line who collectively qualify as experts documented why. (Note, I am not full of myself. This board operates via the wisdom of crowds. Members DStanley, and Ben Miller, commented and edited to help me form a well documented response that would be tough to argue against.)