Given their comments it seems like they're the type of consultant I'd definitely want to record.

I'm certain that in Canada every professional includes an indemnity for recording calls in their engagement agreement. That is to say, you can't record a consultant you've engaged without their knowledge.

Regardless, I stand by my original statement that there are few good reasons to record a conversation without the knowledge of others participating in the conversation.

Just because something is legally permissible doesn't make it right, ethical, or appropriate. Would you record your partner yelling at you? Would you record conversations with your boss?

In almost all circumstances, just a modicum of diplomacy and guile will serve you much better than a clandestine recording.