That sounds linear to me, which is not correct. Injury level is exponential with temperature:
http://www.ncbi.nlm.nih.gov/pubmed/18226454
Injury time is logarithmic:
http://www.accuratebuilding.com/services/legal/charts/hot_wa...
http://www.ncbi.nlm.nih.gov/pubmed/18226454
Injury time is logarithmic:
http://www.accuratebuilding.com/services/legal/charts/hot_wa...
What? Absolutely not. I'm just saying that it sounds reasonable to believe that burns increase with temperature, as opposed to being high in a range of temperatures and lower below and above that range. Figure 4 in your first link agrees with this common-sense guess.
I think it's also pretty clear just from the burn time curve. If it takes you a second or two to notice the heat and move away, then anything above ~155F is going to make a burn much more likely. At 180F, the burn is basically instantaneous. Whereas at 140F, having five seconds to respond gives you a lot of time to move, shake off the liquid, et cetera.
Which makes it sound like there is a lower and an upper bound for this range. That's the issue.
But even with your interpretation, it's true. The upper bound is 212F. A cup of steam is not a significant burn risk, that being something like 0.16 ml of water.