Income reported to you on Schedule K-1, even if attributed to your sole proprietorship or single-member LLC filing on Schedule C, is not brought into your income tax return through Schedule C. Rather, the K-1 is included in Part II of Schedule E Supplemental Income and Loss.
Even though your Schedule C business may be a "member" of the LLC, recall that for income tax purposes, the sole proprietorship or single-member LLC is a disregarded entity, and its income and expenses, profits, and losses, are inseparable from you, the individual taxpayer. Thus, its K-1 is your K-1.
This is logically the correct treatment of income. If the K-1 were reported through your Schedule C, the investment income from the K-1 would ultimately be treated as self-employment income, and subject to 15.3% self-employment tax, even though that income is not the fruit of your labor, but the fruit of your capital investment.