It looks like you are using Flex 4, which, since it is still in beta, might very well be buggy with the layout. In which case, you trying to debug it would be pointless. But I would suggest trying to set the app width and height in addition to the minWidth and minHeight. I know certain Flex 3 containers have issues if you only set the mins.
Perhaps that is the case, but I have another Flex application created in Flex 3, but being edited, maintained and built by the Flex 4 environment that is not exhibiting any problem like this. I've compared settings up and down, but cannot find the difference.
I'm still hopeful someone might be able to tell me what might be going wrong.
I'll answer my own question. Not that this makes any sense, but in order for flex to have scroll bars on children containers, it seems it must be wrapped inside a mx:Canvas tag.... .just for future reference!