You're exactly right: It's a Biostar MB---TH67+ for the record.
I got the computer it replaced out of storage, an HP Pavilon a1350n (Athlon 64x2 4200+), and tried the pctv 800i card in it. Unfortunately, I got exactly the same result. I have an un-updated version of F16 on the old computer; "dmesg | grep "xc5000\|cx88" is identical with that on the newer computer with the Biostar MB.
All of the PCIe cards I've checked look iffy at best, for example, Hauppauge WinTV HVR-1250
A PCI card, the pchdtv hd-5500
is promising to the extent that the outfit that sells it supports Linux. What's not so good is that everything I find about it is really old. Their wiki includes a section on setup in FC2. The kernel module cx88-dvb includes support for the hd-5500...just as it supports my pctv 800i card...
Thanks again for a good suggestion that wouldn't have occurred to me.