No.
Pass through income can be income of any classification. "Pass through" simply means the income is earned within a entity that doesn't itself pay income tax. For example a partnership. If it's an investment type partnership the investment income, be it LT or ST cap gains, interest or dividends is passed down to and reported on the partners' personal tax return. I.e., the item of income retains its character.
If, say, it was law firm partnership then the income is passed through/down to the partners' returns and taxed as ordinary income and subject to self-employment (SS tax).
In your example above the pass through person would likely pay more tax because they would be subject to self-employment which results in doubling your SS tax.
However, this issue is complicated by section 199A, the so-called "qualified business income " deduction.
Fern