BI answers "should people be provided with the necessary essentials to survive".
MW answers "should businesses be compelled to pay a fair market rate for labor", again, unless a specific exemption is made.
Providing BI without allowing for MW still creates an environment in which at least some businesses can game the market to obtain below-cost labor. I see this as a market inefficiency which should be corrected.
The human cost of production of labor isn't zero, which is precisely the point.
If a specific business (or industry sector) wants an MW exception, that's yet a third question (essentially: is the product of this business and/or sector sufficiently valuable to warrant a net transfer of wealth from the rest of the economy to it). My knowledge of economics and markets is such that I don't believe that the free market will allocate resources efficiently in all cases, but where you're going to allow for such a subsidy, you'd best do it consciously, for specific reasons, and as transparently as possible.
Awarding the benefit to large, politically-connected, and highly profitable companies strikes me as a gross market mis-allocation.
If the market clears labor above its minimum sustaining rate, then the MW is a non-issue, but you'd best be sure that that's the case, and if it's a non-issue, then having the MW present changes nothing materially in the market.