Oh no, my school presents it very clearly. I have a subsidized portion, an unsubsidized portion, and a Perkins loan which is very small. My first year here I had to borrow the max due to having to pay out of state tuition (hooray residency) and that max was the Stafford annual max even though it included the Perkins amount as well.
I looked at the link you provided and it provides both limits but it doesn't say that you can borrow the Perkins amount in addition to the Stafford amount. It doesn't say otherwise, but my experiences with the limits say that there isn't some larger limit - just the Stafford limits.