Problem using Maven to obtain Flash Builder 4 Libraries?

Question

My question is related to this one, but is not exactly the same:

http://stackoverflow.com/questions/828960/how-can-i-add-maven-dependencies-to-the-flex-build-path-in-flex-builder-3

Given that Maven will happily download all the correct version of all the swc's of the Flex SDK, it seems that I could point to those from the Library settings of my various flash projects. But whenever I do this I get 100-200 flex build errors that say things like:

'ArgumentError' is undefined.   swc     Unknown Flex Problem
'Array' is undefined.   swc     Unknown Flex Problem
'AS3' is undefined. swc     Unknown Flex Problem
'Boolean' is undefined. swc     Unknown Flex Problem
'Class' is undefined.   swc     Unknown Flex Problem
'Date' is undefined.    swc     Unknown Flex Problem
'decodeURI' is undefined.   swc     Unknown Flex Problem
'decodeURIComponent' is undefined.  swc     Unknown Flex Problem
'DefinitionError' is undefined. swc     Unknown Flex Problem
'encodeURI' is undefined.   swc     Unknown Flex Problem

As soon as I include the SDK in the project library, everything works. Take it out and I get all these build problems.