Community Newsletter: Q&A: Please clarify the digital TV (DTV) transition in 2009

Direct connection to cable is still an option for most.

The signals sent over a cable, going back to the earliest days of cable, have been analog. That is all that there was in the beginning. But since the cable providers did not have to worry about interference with other broadcast services they were able to take advantage of frequency spectrum that was used for other over-the-air services.
Specifically, the original channel 1 was transferred to the use by the 50 Mhz portable radio bands for government and commercial use. So a cable could use a channel 1 signal. Similarly, the gap between channel 4 and 5 and the gap between channel 6 and 7 are used for other over-the-air services.
And there is an enormous gap beween the highest VHF channel (13) at 210 Mhz and the lowest UHF channel (14) at 470 Mhz.

Since the signal losses per foot in a cable go up rapidly with increasing frequency, cable operators chose to pack channels into all of these gaps to minimize the maximum frequency carried over the cable. The result of this was that on old analog TV, without an Antenna/Cable switch setting, could only get channels 2-13 without a cable box. And some of the channels were not recieved well because they were offset slightly from the nominal broadcast frequency.
Once TV tuners were able to receive these cable frequencies directly (basically when electronically-controlled oscillators were introduced instead of inductor/capacitor tuning) you could get all be the pay channels without a set top box. And the way in which the pay signals were made unreceiveable without a subscription and a cable box were not the digital encryption used today but were various distortions of the modulation standards used for that signal.

Short summary:

The oldest TVs could only get channels 2-13 (and not necessarily that broadcast channels of the same number!) without a set top box.

Later TVs could get all but premium channels without a set top box.

Now an TV with an ATSC tuner could get digital signals directly from the cable, if only the cable provider put them on the same frequencies as the corresponding broadcast digital signals, or the TV could tune to the digital cable frequencies. On many cables there is a combination of the two right now.

Any convertor box which is designed only for broadcast will not be able to tune to the correct channel frequencies for the same digital channels through the cable. But the cable provider can still choose to carry some digital channels on the broadcast digital frequency range.