Hi,
to my best knowledge there is no such thing as a free solution for providing
such functionality as a Tivo.
At least most modern cards (DVB-T / DVB-S / DVB-S2 / DVB-C) rely on non-free
firmware files. May be there is a small minority of cards which runs without
non-free blobs but I do not know any. This applies both to PCI, PCIe and USB
devices.
Thus the simplest solution might be buying a free to air receiver for the
system of your choice (DVB-X) or accept the necessity of firmware files and
run a "not so free" system with OpenElec, YaVDR or something like that.
I am more pragmatic here as I have both a cheap DVB-S2 receiver and a HTPC
running YaVDR. Keep this in mind: A GNU Linux PC with non-free firmware on it
gives the user more control over the device than running a closed platfom
like a DVB-X receiver.
This is of course not FSF-compliant.
HTH,
Holger