Parking lot accident - does this sound like there's equal liability to you? My insurance company Geico does?

I parked in a parking lot with angled parking spaces. Along with the arrows on the pavement [the angled spaces also present a big clue] directed you to travel in ONE direction only in the aisles. I was parked in a Nissan Sentra betwn a Honda Pilot to my Left and a Ford Excursion to my Right. Parking lot traffic was to flow from Left to Right across the back of my car. I checked R, then directly behind and then focused L as I began to slowly back out - b/c I am having a hard time seeing beyond the Honda Pilot on my L. As I'm backing out [2-3mph], I feel the crunch. Behind me is a Toyota Landcruiser traveling in the WRONG direction in the parking lot - I'm expecting traffic from the L and she comes from the R. I hit the Toyota's penger side rear tire and side of the rear bumper with the corner of my penger side rear bumper. Geico says I should've seen the Toyota b/c I hit so far back on the vehicle-I say B.S. and challenged them to re-enact to see I couldnt view other car.