Are you confusing access time with download time? When you try to acces a web-page it's like dialling a telephone number - you go through all sorts of connections, taking several seconds, before you are finally connected to the number you want. This is access time. Once you're connected you speak to the person in real time - that's download time. With a web-site the streaming speed may be very fast but you still have to go through all the machinations of connecting, so getting a page to appear on your screen may appear to be slow but it's because of the access time. Fibre broadband will not affect that - it's out of your control.