I've had plenty of application of this issue with venturers who were working on a boy scout rank with their troop while their leadership was in my crew. Also, I was a DC of a den who, to my knowledge, sent no cubs to the troop. Same strategy applies to both types of positions, as their tenure may be used for multiple ranks if they are disciplined with advancement.
Quite simply. At the SM conference and BoR, the scout should be able to describe what he did in that position. What went well, what didn't go so well, what he'd do differently. Early in a scout's tenure as an officer in my crew, I encouraged his SM and CC to ask those questions. When they did, it helped the scout get a dose of accountability for his office, and it help share ideas between youth in different units.
Pro tip: where should an SM look for "demonstration" of a DC fulfilling his duties?
Talk to the cubs in the den. Ask one simple question: "What's the name of your Den Chief?" In addition to hearing your scout's name, check for smiles on the boys faces as they say it.
At round-table talk to the Cubmaster (and, if possible the Den Leader). Same question, but rephrased. "Which of my guys is your Den Cheif?" Listen for the answer, check for a smile.
If you see an eye-roll, frown, or the slightest ambiguity in those responses, it's time to have an impromptu conference with your scout.
Training benchmarks and attendance check-lists are nice, but they can be deceiving. For example, a busy den might meet too frequently for a DC to keep up, but if he makes a point to show up when the DL's gonna need him the most, he/she will literally worship the ground he walks on.
I don't think I have ever seen the question come up. As far as I know all Scouts in our troop who have been den chief (and there have been many) have done it for at least one full Cub Scout program year (basically the school year) and often for more than one year. It is generally considered to be a one-year-at-a-time job. We have had Scouts who have had another position for at least part of the time that they were also a den chief (leaving one to wonder how good a job they did at either, but as far as I know nobody has ever been refused a signoff for a POR in my troop.)
To Eagle94-A1's point, I didn't not mean to suggest that one can earn the Den Chief Service Award just for showing up for a year. I do not know how many other Scouts in our troop have earned that award. I know my son did. He did do the Den Chief training (in person, because I drove him there along with a few other Scouts from the troop; it was not "online" back in the antedeluvian days of 2006 or so.) I have a suspicion that some of those other requirements may not have been there 12-ish years ago, but whatever the requirements were, the den leader determined that my son did them.