What does it mean when insurance company says it is word vs word case deny liability and find fault free?

Answer 1

Essentially, this means that the (two or some other number) parties or participants in an incident have conflicting accounts of how the incident happened. Inherent in this characterization is the fact that there were no independent witnesses to the incident to support one side or other, or that whatever witnesses that do exist give equal credence, or equally believable accounts of the dynamics. Further, it refers to the fact that fault or liability on one party or the other cannot be demonstrated by physical evidence (such as areas of impact, paint transfer, or other elements of damage to the vehicles involved in a collision).