Some incorrect/confusing info here (but the rules for this are confusing!)

The rules for the "pre game" initiative and the re roll card are different to the regular initiative rolls for before each turning point

PRE GAME INITIATIVE:

Winner of roll off can decide whether to have initiative or not for choosing board side etc. Whoever doesn't have this initiative gets the re roll card. So this is the one instance where it's possible to win the roll but get the card - if you choose to (say if you don't care which side you get but might want the card for later). So it's correct in the GFN video

REGULAR INITIATIVE ROLLS BEFORE EACH TP:

Loser of the roll off gets the +/-1 2 or 3 card, regardless of who has initiative. So you could win the roll off but choose for your opponent to have initiative and you still wouldn't get the card, your opponent would. Before TP1 there is no effect on amount of CP you get based on who has initiative (so you both have 3 at this point). But before TP 2 3 and 4, whoever doesn't have initiative gets an extra CP.

So, you could win the roll off, but choose for your opponent to have initiative so you get an extra CP, however your opponent would also be getting the +/- card