It's well known that Klopp and/or the club's senior execs speak to Mike Gordon, the second largest shareholder in FSG, on a daily basis. https://twitter.com/SurMerco/status/1288102740975955971?s=19
Moreover, there's nothing inherently wrong with an ownership group that has an "arm's length" relationship with a club, provided they e.g. establish solid foundations (yes), hire some of the best talent in business/commercial ops (yes), and world class technical staff (yes).
That leaves the ownership group to focus on helping to manage crises if and when they occur (they have, and they did), as well as delivering on bigger picture projects like stadium and training infrastructure investment and agreeing to substantial player purchases (also, yes).
Which isn't to say that certain issues couldn't have been better managed, or even avoided completely on the basis of being their own mistakes (which, to their credit, they also willingly recognise and acknowledge). But in any case, they're objectively *excellent* owners.
SAF said it pretty much perfectly when speaking about Klopp and the LMA Award - his "personality runs throughout the whole club", and Klopp himself defines leadership in part as "have[ing] strong people around with a better knowledge in different departments than yourself."