Detect magic and a good spellcraft check will reveal the nature of their ring. Note this is often effective against shapeshifters and magical disguises as well. You know the dude with an illusion effect on him is hiding SOMETHING, even if you don't know what.
Detect Good generally reveals that the supposed Blessed Priestess of Light (who's actually a succubus) is definitely not normal. Not damning evidence but more effective than detect evil when the villains get wise to it.
Cheerfully handing the subject one of those "immediately gives wielder negative levels" magic items tends to have noticeable (and highly amusing) results.
The above was used to great comedic effect against a necromancer one time. The int-dumped Paladin with a wand of healing had been conned into believing that the necromancer's undead minions were living hirelings, so of COURSE when they got hit he "helped" them. Cure, cure, why he no more no more? Holy water does this as well and also effects evil outsiders.
Potentially there is some rule about higher level spells "punching through" lower level defenses, like how a heightened continual flame can beat deeper darkness. Or the DM erroneously believes this to be the case.
The ring will prevent you from being detected as evil, but you are still evil. You will still be affected by spells that affect evil even though you cannot be detected as such. So someone using detect evil on you will not detect you as evil, but holy smite will still damage you. The ring only affects you so anything that is not limited to yourself still detects as evil.