I believe their characterization is accurate. Not just anyone can download files from VT. You have to have access to their private API which is a premium billed (and anecdotally very expensive) service.[0]

That, to me, qualifies the term "VirusTotal and their partners" as accurate, since this is only a select group of companies who are paying VT a large sum for access to the data.

[0] https://www.virustotal.com/en/documentation/private-api/#fil...