This is how darkmoon invasions work.
( X +/- (10 +/- (10% of X))), where X is your current lvl. This means that, for example, if you're level 50, you can invade people from lvl 35 (50 -15), to lvl 65 (50 +15).
What this means is a sl 120 DM will invade eligible players between 98 and 142, invading whomever the search finds first. ONLY if no eligible hosts are found, will the DM invade lower. The same can be said of the red eye orb, but replace "lower" with "higher". This means that in relatively sl specific invasion areas like the burg or the painted world, being above sl 120 does not increase your chances of invading, reguardless of the orb used. DMs can invade farther down than others can using orbs, yes, however in my experience and the experience of several others I have talked to, it is not common to invade outside the regular sl range unless you're seriously overleveled for the area (sticking to 120 and the burg as examples, a dm would likely need to be above sl 150 to be regularly invading out of the initial formula, and such invasions would be slow) or invading the same 1 or 2 low sl people repeatedly, in which case simply reloading the save will often fix the issue.
There is speculation that the amount of sin a player possesses modifies the formula, but I haven't seen proof of this.
There accusations of DMs invading supposedly sinless characters. I will remind everyone that the bottomless box transfers sin, and that indictment sin cannot be absolved.
There is also a variant of the glitch at the link below that has the occasional summon or dark wraith invade as blue. If I can find a video depicting the variant I will update the link.
https://www.youtube.com/watch?v=CEmn3J_k1iQ
The Darkmoon summon ring works essentialy the same way the cat covenant ring works, the only restriction is that the host must be in dark Anor Londo.
There are players who cry foul that DMs get the strongest buff in game. I must remind these players that magic defense is far easier to boost than the lightning defense that sunlight blade acts upon, and many armors have better magic defense than lightning. There are also 2 sorceries and 2 miracles that cut magic damage and none that cut lightning damage. After testing, and verification, dark moon blade only does between 10 and 80 more damage per hit than sunlight blade, and as previously mentioned, magic is easier to mitigate than lightning.
Wrath of god is hardly DM exclusive, players using it are a dime a dozen, dms using it are simply making the most of their covenant choice.
Finally, I have heard the odd mention of DMs invading hollow because they're afraid to lose. I must point out that invading hollow is no different than invading in an area with a dead boss except that DMs can invade hollow in the kiln, and neither speak of the character of the player.
Hope this helps.