You seem to be confusing some things.
Yes, the light in a fiber optic cable travels at the speed of light in the medium (glass fiber), which is slower than the speed of light in a vacuum.
Where I think you are confused is that a sending device will only serialize data onto the fiber at a given rate. A 1 Gbps interface will serialize 1,000,000,000 bits of information in one second, so the first bits are arriving at the destination while the last bits have not yet been serialized on the fiber.
When sending data on a network, the data must be framed so that the receiver knows where the data start, and where they end. The data must then go up through the network stack at the receiver, be processed, and a reply generated and sent back in the same way the data were sent in the first place. All that adds a lot of time when comparing the latency of a ping request/reply.
The request data end up going through two network stacks and the length of the cable, being serialized/deserialized at whatever speed the interface does, and travel the length of the fiber. The request is processed, a reply is generated, and it must do the same thing the request did. The reply is processed, and the time difference noted. The speed of light plays only a very small part in all that.
Also, using copper cabling will result in basically the same time as fiber optic cabling with the same serialization rate because electrons move through the copper at the speed of light in the medium, and that is very close to the speed of light in a glass fiber.