Never doubted that the other guy changed lanes into you. Unfortunately in OH it doesn't matter much - guy in back is ALWAYS guilty. Sounds like your insurance has the same short sighted opinion.
From my days with race cars I can tell you good braking depends on the entire vehicle. Tires, brakes, springs, shocks, suspension geometry, all of it. With all things right, the lighter vehicle will stop shorter - every time. Folks are not willing to pay for GOOD brakes, either in money or harsher ride. Until you drive something on 12" sticky tires with huge brakes, steel braided lines, properly biased pressures, correct shocks and stiff springs you just can't believe how a vehicle can stop!! Passenger vehicles have WAY too much compliance in hoses, springy calipers etc. Makes for a mushy pedal with poor feel. That kind of system plus low skill drivers brought us ABS systems - which can NOT stop as good as a skilled driver! They DO cover up for the 90% of folks who can't use their brakes to maximum capability.