Hello,
Thank you all for your responses.
Yes, Aegishjalmur, this is what I understand. I am now surfing on the FNF Canada website in the hope to find out black on white about this procedure. Or if I could have a communication coming directly from them (not going through my mortgage broker), that would, I guess, be sufficient to lower my concerns (they are a very large corporation, so I guess this means they are reliable; I try not to be cynical or leaded by fear while being ignorant... but not stupid either...)
So yes, Sibley, SwordGuy and Linea_Norway: I really want to feel safe before signing anything. Yes, I could wait another month, but I doubt I could have such a good rate. Again, many thanks, Mustachian's advices are precious.