It’s not a question that Vanguard engaged with boards of the companies they interact with and it’s a pretty commonly cited concern in corporate governance circles. So much so that the big index funds are piloting giving their votes to fund holders.
The conspiracy theory issue here is that the poster is a) expressing something much more nefarious by implying Starbucks debt is part of a plot by vanguard/Blackrock b) setting up Musk as a white knight fighting these nefarious forces and c) citing fabrications as facts to back up the claims, then devolving to much less striking claims (“big shareholders have influence”) when called on it.
This has all the hallmarks of a classic conspiracy theory.