When two (or three) different sources give differing values for WAR for a player saying "It's better than anything else", that's a pretty low bar. As you said, every calculation that gets put into WAR is flawed in one way or another so I'll ask it again. When does it become "garbage in, garbage out"?
I guess that's a personal decision.
My opinion is this: while the numbers fed into the system may be imperfect, they are not garbage. When the sample sizes are large enough, most things have a way of evening out, such as bad scorer decisions, strength of opponent and other factors.
All I'm saying is that WAR represents the best number I know of that shows a players overall value and not just hitting, power, defense, running and more...
I'm sure teams have their own formulas, and my guess would be that their results would be pretty close to WAR, in terms of comparative player value.
If you are the type of person that thinks this is not possible or not something you even want, even if "perfect", then WAR would be worth 'absolutely nothing!"
To me, it has value, but it is not the be-all-end-all.