In your scenario, the K-1 *SHOULD* be issued to the John and his Social Security Number.  It is not supposed to be in the name of the disregarded entity or its EIN.  The same applies to 1099-MISCs and other informational forms.
https://www.irs.gov/instructions/i1065#idm140242267679120

Ideally, if you receive a K-1 (or 1099-MISC) in the name of the disregarded entity, it should be corrected.

I think the OP's situation is sort of the reverse.  The Partnership owns a subsidiary business (the disregarded entity).  Although it might need an EIN for non-income tax purposes (such as employer forms), for any income tax purpose it should use the EIN of the owner (in this case, the Partnership).