Again then... when do you use character level to determine DC?[
To be pithy : always, and never.
Always - your role as DM is to set the scene, part of that is to decide the level of challenge (chance to succeed/fail) something offers. The suggested DC values in the DC-by-level chart offers generally reliable values to represent 3 broad difficulty levels.
So, you can reference the players' level(s) and then, you have guidance as to which values of DC will offer the difficulty type you want.
Never - if the "thing" you're trying to stat is well defined in the fiction, then the DC comes from that fiction based upon your world axioms. If it is appropriate as a challenge for the players or not, is then a secondary question - it is there, you have spent time putting it there, having the players interact with it.
What the rules tell you (by this I mean, the DC setting guidelines) is that, if you stray very far from those suggestions, you may find yourself in a situation where the challenge is trivial (then, why waste time stat-ing it up?) or impractical/impossible for the PCs to interact mechanically with (then, why waste time stat-it up?).
The difference here with 5E is a question of reliability/predictability, and granularity.
R/P - the bonuses in 4e are much bigger than in 5e. Thus the d20 has less weight = more predictable outcomes.
G - in 4e, the chart offers values for every single level to maximize the above point. It would still work (possibly better in some regards) if you used the same approach as 13thAge. 5E decided to use steps of 5 and qualifiers since, progress in skill values is both slower or "null".
There is a basic difference in the assumptions of 4e and 5e when it comes to skills - in 4e, your experiences are considered to have you grow in all aspects. In 5e, you grow only in aspects on which you actively spent resources on at some point.
Honestly all you've shown to me, in the convolutions to avoid using character level to set DC's, is that 4e is unnecessarily complicated in its methodologies and subsystems for setting a DC... I thought this system was supposed to be easy for new DM's...
So to determine a DC you can...
Use character level
Use an objective DC
Use a series of DC's based on the level of a skill challenge
Use the defenses or stats of a creature
Use the level of an encounter
Does that sum up all the different ways of determining a DC in 4e?
... dude... it's like you're looking through a telescope by the lens side.
There are 2 ways to set a DC suggested by 4e. One is encouraged for its ease of use, the other is encouraged for its power of world-building. You can use both, you can make mistakes in both, both can be awesome, both can suck.
1 (level based) - look at "thing" number(s) (i.e. level) and set DC based on % you want.
2 (fiction based) - look at game numbers, chose "thing" and set DC based on % you want from that.
Once you do 1 (compare with expected numbers), you've set 2 (fiction). Once you've done 2(fiction), you've set a level for 1(comparable numbers).
[sblock="Not really useful"]
Use character level - if you want to have a DC that offers a set level of challenge, you need this info. This is system agnostic : you will
always need to know the players' approximate numbers to set numbers yourself if your wanting to create a specified difficulty.
Use an objective DC - as I first pointed out, you do this
always and never If you've already set the fiction, then you've already set the DC. If you've set the DC, then you've set the fiction - the idea of the same wooden door having a variable DC is false.
Use a series of DC's based on the level of a skill challenge - if you've set the level of your SC, then the suggest numbers are those that offer the greatest chance for the desired outcome. This is kind of asking if you use a monster's CR to set it's values in 5e.
You can set a CR and use appropriate values, or you can set the values and reverse engineer the CR - you can do the same with an SC (it's not common practice, but you could).
Use the defenses or stats of a creature - then it's already set... so there's no setting it...?
Use the level of an encounter - if you want to offer a consistent presentation of the situation as having a difficulty of X.[/sblock]
TL;DR
LEVEL is the gauge of "power".
If you want something to be of LEVEL power, then you use LEVEL suggested DCs.
Do you use LEVEL to set the DC :
Yes - you're building a challenge of LEVEL power
No - you're building a challenge of NOT-LEVEL power
This works in 4e because LEVEL is a fairly accurate representation of the numbers.
This works differently in 5e because LEVEL has less to bear on the numbers, and those numbers are smaller, so the d20 has more to say.