alt Hacker NewsThe article is pointing out that one of the base assumptions behind fMRI, that increased blood flow (which is what the machine can image) is strongly correlated to increased brain activity (which is what you want to measure) is not true in many situations. This means that the whole approach is suspect if you can't tell which situation you're in.
fMRI ususally measures BOLD, changes in blood oxygenation (well, deoxygenation). The point of the paper is that you can get relative changes like that in lots of ways: you could have more or less blood, or take out more/less oxygen from the same blood.
These can be measured themselves separately (that's exactly what they did here!) and if there's a spatial component, which the figures sort of suggest, you can also look at what a particular spot tends to do. It may also be interesting/important to understand why different parts of the brain seem to use different strategies to meet that demand.