This is obviously not true. You have to look at the different materials cars or bicycles are made from because that statement doesn't restrict itself to a specific material.
This would require the rubber of 200 bicycle tires to be at most the amount of rubber used to make a car. Most of that rubber is found in the tires of which a car has 5 (let's give it a spare tire). Therefore you needed to be able to make about 40 bicycle tires from the rubber used to make a since car tire – which obviously by looking at the mass alone doesn't work out.
Since someone actually disputes this, here are some sources.
You can find here that a car tire has a mass of 22 pounds (9.98 kg). The page also states how a car tire is composed. It's 41% rubber which means that one car tire has 4.09 kg rubber. Therefore, each bicycle tire had to have 102 g of rubber or less. You can take from this page that the inner tubes alone have about that mass and the shells even add about twice that 102 g to the total mass of the rubber part of a bicycle tire.
You can find out from the first link that there isn't much other than rubber and carbon to the rubber part of a tire. But for the numbers to match up, more than two thirds of the rubber parts stated above had to be something different than rubber.