Can a designer get hold of the PCI Express specification without being a member of the PCI SIG group?
Technically, no.  Of course people will pirate lots of things they shouldn't.

You get more than just access to the spec for that $3K.  You get a PCIe Vendor ID number, which is required if you want to make a product that uses PCIe.  

But...  Do you really need the official spec?  Probably 90% of the spec is only useful for people who are designing chips (not even FPGA's).  Do you really care about the low-level signal encoding, or the more esoteric state machines?  If not then there are books on PCIe that will likely be more useful to you than the spec will be.  PCI Express System Architecture is one such book that can almost replace the spec, but there are many others.