Wow, this is a blast from the past. You watch a documentary and decide to dredge up this debate from back in the day? Polar exploration is an interesting topic, especially from the 'they went a long long way away and then died' perspective.
From what I remember of my reading on the issue, the biggest argument 'against' lead poisoning is that the expedition slowly died over time instead of everyone dropping at the same time.
How the expeditiion moved and the truth of the various (some impossible) Inuit oral traditions are almost unverifiable. I've seen some very strange ideas pitched based on very odd things like the position/orientation of boats and cairns.