I too turned on mayhem as soon as I got to sanctuary in tvhm and did not have to wait until the story was complete.

There is 0 useful information in any of your sections.
How about numbers - stats - modifiers anything that would be remotely useful.

Pc need to complete story mode to acces TVHM

It seems that PC players have immediate access in TVHM where as console players dont

I did not have to clear the story in TVHM to get mayhem, it was already there.

Nope, it's there

Yes you do I am in tvhm for the first time and it is not on sanctuary

You don't need to clear TVHM to unlock Mayhem for it.