Woolf University

[Eleanor]

That's correct, Woolf really isn't an institution or school itself, they partner with institutions globally to provide education at an affordable rate.  In any case, I would review the details and info within the post #2 link to a previous thread.  They may have added partnership institutions, you should also investigate the partnership institutions for proper accreditation in the country.  Other than that, if they're accredited, they are fine, these shouldn't be thought of as a scam just because of a few iffy points.

I might be missing something here - if Woolf itself is the degree granting institution, why would the accreditation status of their partnership institution matter?

It can. Woolf has institutional accreditation (licensing) as a Higher Education Institution in Malta. Unless having University status, they are not autonomous in designing and self-accrediting programs (like the University of Malta). Consequently, they must get at least one program accredited. Their accredited programs are listed on the MFHEA database. However, there is no requirement to have all offered programs or courses being accredited. An institution must only clearly mark and distinguish those accredited from the non-accredited. 

Program accreditation in Malta (and I guess everywhere else) is specific and strictly attached to the submitted program accreditation application: 
- program structure
- course outline
- syllabi
- learning outcomes (!)
- learning format
- LMS (if online)
- systems and processes
- quality assurance
- language of instruction
- place of instruction
- ECTS credits
- etc. 

MFHEA does not accredit degrees, but programs. Woolf or one of their network colleges may very well offer an MBA program, which does not reflect the accredited version. This is where I see potential conflict and wondered earlier if the Upgrad version of the MBA is also the MFHEA accredited version.