In watching a lot of online dnd 5e it seems many DMs tend to grant more information or offer a greater degree of success when the skill check far exceeds the required DC. I believe skill checks are intended to be a pass or fail type test therefore the degree of success or failure should not matter. Do I have this wrong?
Most of the time, skill check outcomes are a binary pass/fail, but even RAW has exceptions. A Ghost (MM p.147) has this ability (emphasis mine):
Horrifying Visage. Each non-undead creature within 60 feet of the ghost that can see it must succeed on a DC 13 Wisdom saving throw or be frightened for 1 minute. If the save fails by 5 or more, the target also ages 1d4 x 10 years.
Even outside RAW, there are guidelines for applying the same concepts to other tests. Resolution and Consequences (DMG p.242) lists optional measures the DM can elect to offer or use (emphases mine):
SUCCESS AT A COST: ...When a character fails a roll by only 1 or 2, you can allow the character to succeed at the cost of a complication or hindrance. Such complications can run along any of the following lines... A character fails to intimidate a kobold prisoner, but the kobold reveals its secrets anyway while shrieking at the top of its lungs, alerting other nearby monsters.
DEGREES OF FAILURE: ...A character who fails to disarm a trapped chest might accidentally spring the trap if the check fails by 5 or more, whereas a lesser failure means that the trap wasn't triggered during the botched disarm attempt... Perhaps a failed Charisma (Persuasion) check means a queen won't help, whereas a failure of 5 or more means she throws you in the dungeon for your impudence.
CRITICAL SUCCESS OR FAILURE: ...rolling a 1 on a failed attempt to pick a lock might break the thieves' tools being used, and rolling a 20 on a successful Intelligence (Investigation) check might reveal an extra clue.
Often, when published modules specify Knowledge checks (this one I don't have a citation for, unfortunately), they'll have a written table a player rolls against, where they get all the information up to the result of their check:
- DC5: It looks like a goblin banner
- DC10: The symbol belongs to this particular warlord
- DC15: He had his own symbol code for secret messages, this one says something
- DC20: The coded message is "there is a traitor in our midst"
This is somewhat discussed in the DMG on page 242. It suggests that a failure by 1 or 2 (or exactly hitting the DC) might lead to a success, but with a complication; and failure by a wide margin might have more serious consequences than failure by a smaller margin.
There's nothing in there about degrees of success, but there's nothing to say you can't or shouldn't do that, either. There's nothing wrong with giving more information or better results from a very high margin of success. It's entirely within the DM's purview to make judgements like that.