... If the cable system has a fiber-optic feed from the broadcast OTA station and that same OTA station has a bunch of subchannels, it is entirely possible that the QAM HD cable feed is superior.
Technically it is "possible", but quite often (if not always) not "entirely possible", because that is somewhat academic. In the real world, that's not really how things work.
The fiber feed sent to cable is typically already shaped and encoded at whatever rate the TV station is also using for that same signal that they broadcast. In fact, it is the same signal. TV stations do not encode differently for their transmitter exciter than they do for direct closed fiber feeds to cable and sometimes DBS, because there is no motivation to do that. In fact, quite the opposite; it would cost much more, decrease QoS reliability, and add to complexity and maintenance overhead. Some stations receive their network signals already crunched down, precludiong them completely from even entertaining the thought.
TV typically encodes just once, to fit SMPTE310, and that same signal gets sent usually via an ASI stream, sometimes via TCP/IP, via fiber to secondary cable vendors. Everybody gets the same signal, and the same PQ. Cable demuxes the channels of interest and eventually QAM modulates them, both processes being completely transparent to the data that comprises the picture and sound information.
Sometimes they further compress, but rarely, and this means that cable can and usually does duplicate the PQ of the OTA signal, because the binary coefficients that represent the pixel information are never modified and they stay unchanged within the digital domain until they get to the decoder in your STB. If the math is not changed, the PQ can't change. Unless a zero can magically turn into a one, or vice versa
, everything stays locked exactly the same, and since math is an abstract construct, there is nothing within the hostile transport environment that can achieve that.
In analog, the message is intimately tied to the medium, and if something degrades the medium, it degrades the message along with it. In digital the message is not tied to the medium (that abstract construct thingy once again) meaning that the medium can be degraded, up to a point, without that touching or altering the integrity of the message, even a little bit.
There is jitter, but that gets reclocked in the decoder. There is carrier degradation, but not information degradation. A written note with a phone number on it can go through the wash and bleed and smear, but if you can still extract the information by reading it, it is identical to the same information used to write the number down in the first place, for example. You still have all of the information even though the medium carrying it to you might be degraded, and that is the analogy here.
The message is not the squiggles on the paper, instead it's a number, which is also an abstract construct rather than something that exists in the physical realm. If one or more of the digits in that note are degraded too much to make out, the entire information is invalid and you can't call the number, which is the same analogy as the digital cliff, where you either have all of the information intact, or none of it, like when the signal degrades enough for your screen to mute to black. If you can make out part of the smeared digit and make a correct educated guess, you then have the entire information once again, which is the analogy for error correction.
DBS is a little different because of the added MPEG-2 to MPEG-4 step, which adds inevitable rounding errors to the information, which alters the binary math slightly, which potentially can manifest as PQ degradation. But both DBS vendors seem to do it cleverly enough so that we generally don't see the difference, regardless of how closely we look or how golden our eyes might be.
Bottom line, it makes more sense to record the signal via sat and save HDD space than it does to record it OTA. The trade-off is the potential degradation in the conversion process, but if done right and you can't see the difference, the smart move would be to forgo OTA for DBS, assuming you have both available, unless recording space is so abundant so as not to need management, which it never is.