Sadly, there's more in an FPGA than "just" a dumb lookup table for implementing logic functions. There's not much more reason to trust an FPGA than an Intel CPU.
Maybe you have any links with a good further reading on that topic?
Well, in theory it must not, because it could detect "oh, this looks exactly like one of popular Ethernet cores, so I'll bug onto those pins and have networking", but this seems like a hard task. Or, well, it could be that every pin is hooked and a secret block awaits a specifically crafted code (somehow like port knocking), but I'm not sure this is a feasible approach.