No, you must not. The energy required for the car to drive 12kms is 996 Wh. let's round to 1kWh.
Solar is DC. for instance Tesla powerwall is 97% efficiency for DC/DC conversion for charging its battery. So you need basically 1kW of solar to produce the needed energy to drive 12km (per hour). I think you are off by at least a factor of 3.
edit: at 20% solar efficiency that would require 5m^2.
No, my claim is that their solar claim is not ridiculous ;)
Also, if I do the math on their AC charging. 35km/h gained --> 2905Wh energy. Standard 230AC, 16 amps is 3680W. So I guess the number there is also correct? Take about 85% efficiency, then you have 3000Wh in one hour from 230V AC