Basic technical question about digital source signals

So, the quick answer is it is smoothed. Yes, there are discrete samples. But filters reconstruct the analog wave form, essentially via low pass filtering.  At the recording studio a similar set of filters is in place to ensure that nothing above the cut-off frequency (let's not get too deep here) is captured -- which can mess up the entire process.
Basically this si what a DAC does.  It converts Digital to Analog. There are different methods, but step #1 is to create a PDM or PAM output (one's a stair-step, one varies the density of equal height pulses just like fuel injection). The 2nd step is to smooth it out and remove the hgih frequency noise.  All of this was figured out int he 1960s, mostly at Bell Labs for long distance telephony.

The results are very good, but nothing is perfect. The analog amplifiers and filtering were among the first places addressed for improvement when digital first came out int he 80s. Not only are analog filters in place, but nearly everyone uses digital filters on an over-sampled signal.
When you over or up sample a signal the goal is not to magically create missing information from a vacuum. Its simply to move the noise ("steps") to a higher frequency so that they are more easily filtered out. Get i hgih enough and your ear will do it on its own.
You can perform normal measurements  - noise, distortion, etc on a the analog output of a DAC.
G

Given the number of people who prefer nonoversampled DACs something seems wrong/incomplete with this theory

Well, first, i’m providing a technical answer. You need not like it, but it is true.

Next, people have many opinions. Many are odd. Many will disagree. Look at politics.

Third - done right i clearly DO like it, ad anyone who listens to bitstream or DSD is listening to hugely over sampled streams by definition.

Fourth - we have no idea what was done in the anti-alias filter; that occurred in the studio. oversmapling was almost certainly employed, statistically, but we don't know. And aliasing is NEVER a good thing. It creates (maybe) tones that never existed in the first place.

I cannot personally imagine how allowing hgih frequency junk through, or having brick-wall,phase incoherent filters can possibly be preferable, but hey.
G

such a design decision breaks the theory of digital audio.

Not really, it presumes that subsequent filters (mechanical limits in your speakers and your ear, which respond per F=MA; inherent limits in subsequent components) achieve he filtering.  There will be no aliasing after the DAC.  Yes, there could be HF noise residue; but hearing is highly attenuated above 22 kHz (if present at all) anyway.

Just as a design decision not to band-limit the input breaks the theory.

That would truly violate Nyquist's paper.Without band limiting various forms of aliasing and their effects can occur. 

Really quite different