The chromosomes look very similar, yet when comparing human chromosome 2 to the ape chromosome, where human chromosome 2 is joined looks very different; here's a detailed picture https://1.bp.blogspot.com/-kkvF0n_ssLA/UaYUSoguxaI/AAAAAAAAGOs/HUV8ZoLUaos/s1600/1982-Chromosome2-small.jpg
There is a case for fusion, yet I remain skeptical because they remain very different from each other at the point of fusion, which also undermines your analogy about the parked cars, but I'll use it because it has some merit. In the analogy you cited, if the car in front had scraped your car's front bumper, there should also be a scrape on the other car, but you never mentioned that and cars can come in the same color; it's likely but the way you described it it's also possible the car that scraped yours left and another car the same color came in and parked there.
Not to mention the fact that the chromosome didn't join in chimps and chimps are still around, so why didn't they "evolve" and why did we "evolve" even though we live/lived under the same conditions?