If a door is DC 26 regardless of tier, they could very well be the same door in fiction. And a Paragon tier PC might be expected to be at 7(level)+5(training)+6(stat) or +18, so needs an 8 or 65% of the time where the Epic Demigod might be 12+5+8 or +25 and therefore auto-succeeds. Hmm — Hercules shatters a door that Lancelot might have some issues dealing with? And what about that Epic Wizard with +12 from level vs a Normal Wizard 1 with a -1. That Epic Wizard might open the door 30% of the time! But 0% of a DC 33 door that I might expect to see for a 65% chance of success.
Three things are going on here:
Either we're in a skill challenge or we're not. A DC 26 door is not really an appropriate challenge for a 24th level Strength PC. If we run into a DC 26 door, that's really to make the Fighter feel good about himself and is not meaningful to the encounter. The rough equivalent here is throwing a DC 10 door in the way of 20 Strength Fighter who has at least a +4 from Proficiency. Sure, you can do it if you want to do it, but it is kind of pointless other than again, to make the player feel good. If you want to challenge an Epic Str PC, you throw a 33 DC door in their way just as you throw a DC 15 door in the way of a 20 Str/+4 proficiency PC.
So that Wizard having a 30% chance of succeeding — and in fact probably can succeed regularly against Heroic tier checks, what's going on there? Well, he's a freaking Wizard. We could define that he has cantrips of Jump and Open Door that he can just casually pull out of his hat. Or maybe he has some undefined magical trinkets that assist with Strength checks. Or perhaps he's learned how to redefine the universe in such a way that the door weakens in his presence. The important question to answer this if necessary is what is the fiction that's fun for the entire table. I'm perfectly okay with the Wizard being defined as having access to some minor cantrips or magic items that don't really see a lot of use as long as my Demigod Fighter is significantly better than him and shines when the focus is on feats of physical prowess.
5e using 4e/2 math means this stuff happens all the time in 5e. So as an example, my 1st level 8 Strength Wizard has a 25% chance of opening up a stuck DC 15 door where a 20th level 20 Strength Fighter might still fail to open it 15% of the time. Note that my Epic Wizard has no chance of upstaging the Epic Fighter when meaningful checks are being performed. The Wizard will auto-fail at that point even if I have a 30% chance of opening a door we'll never see in a meaningful check environment such as a skill challenge.
------
So to sum up — static checks are for non-meaningful checks. Changing DCs to challenge the PCs is for meaningful checks. A DC 26 door is always a DC 26 door in 4e. If the correct check is for a DC 26 to challenge the PCs in a skill challenge, then that's where you might find it. If the correct DC is 27, then the door got changed or modified or there'll be a slightly easier check somewhere else in the adventure.