Just seen this post, good to have you back!
Just a thought about the bit I've highlighted, I'm not saying your making it up so don't get me wrong. But, for me, as a business owner myself, I've never actually put anyone on "gardening leave", I've had to sack a couple off, but I haven't and would never tell any of the other members of my staff the reason why. Basically, I'm not sure Klopp would have actually told the players the reason why Buvac is not around. I get the feeling your neighbour could just be stating the most credible reason we've all read so far.
I to have my own business and comparing my approach to H.R. to LFC's approach to staff employment and contractual matters are separated by a massive delta.
When LFC places a contracted member of staff on "gardening Leave" they have many aspects to consider:-
Timing (crucial strategically at the moment)
Media (fake news, speculation etc.)
Contract ( Gagging clauses, financial severance etc. etc…….)
Often a period of enforced agreed leave is the best option, it could be viewed as a cooling of period, for a more timely and strategic approach to making it formal (end of season proper)
As for informing the playing staff I would imagine that the last thing that Klopp and the club would want to engender would be Chinese whispering campaign in the dressing room. Also bear-in-mind, Buvac was in one to one contact with the players on a daily basis, therefore I would guess "bullshiting" and smoke screens was not an option.
If I was JH, which of course I'm not! This would certainly been best option, at least in the short term, to handling this potentially de-railing debacle.
As I ended in my original post. Make of it what you will.