Last mile connectivity for fiber connection

I just called their office, and they said that with fiber, I would need an adapter at my house, so copper is looking much better in that case. They also said that I'll get symmetrical connectivity no matter if I use copper or fiber. Are they bullshitting me then, or is symmetrical connectivity over copper possible?
 
This is how I think it will work:
Fiber goes to panel.
Ethernet cable from panel to a computer/router.
So, it will not matter if the panel is on your property or the next property.

Symmetry is possible over ethernet. What's inside the ethernet cable? Copper.
That's why they're saying that you'll have symmetrical connectivity if you use copper or fibre.