I don't see any reason to doubt. ForgeFPGA is said to be successor of GreenPAK, and GreenPAK tools are capital F free. Get it from https://github.com/azonenberg/openfpga.
It's really surprising for any player in the IC design world to publish anything using free software. Normally the software is proprietary and costs $10k/seat/year at a minimum.
You're not wrong, but it's important to keep in mind that for more complicated FPGAs, they have hard IP blocks in them often supplied by other companies. Also consider that when these IPs have errata in them, they can sometimes be worked around with FPGA soft logic. Oh, and parts of the software are supplied by companies like Synopsys.
As far as I am concerned though, Synopsys is essentially Autodesk, and Blender is taking over!
$10K/seat/year? That's a fantasy. Maybe if you just want to look at a schematic. As soon as you start actually doing something useful the price per seat goes way up.