Take a spell like Stoneskin. One of my BBEGs (I'm a DM) cast Stoneskin on themselves to maximize their tanking capabilities. Our party wizard asked about Dispel Magic, and if it could be used to dispel the effect. In the end, it seemed RAW, so I let him. Though later, this seemed... weird. Stoneskin technically has 3 effects (resistance to 3 different damage types) and the target was the source of the concentration. Dispel Magic removes one magical effect, not one spell.

In the future, my personal ruling is you cannot end an effect if their concentration is on themselves. The wizard seemed surprised when I let him end it before, so I think he'll agree it seems reasonable. I'm comfortable with how I'll handle this in the future. I'm just curious if there are Sage Advices or Errata covering this that neither of us have seen.

Dispel Magic ends Stoneskin

Your original ruling was partially correct - here's how it should have gone down:

Dispel Magic states (emphasis mine):

Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends.

The target creature currently has stoneskin active on it. This is a 4th level spell.

If dispel magic was cast at it's standard 3rd level, it would require a DC14 spellcasting ability check in order to end it per dispel magic:

For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell's level. On a successful check, the spell ends.

If the caster of dispel magic knew that stoneskin was up and could cast it at 4th level, they could dispel it immediately.

The number of spell effects don't matter, it's the spell itself that is dispelled.

What about Concentration?

Concentration doesn't matter. What matters is the location of the spell effect and not who is concentrating on it.

What about multiple spells?

In the case of multiple ongoing spell effects, a single casting of dispel magic can remove all active spell effects on the target.

Going by RAW, Dispel Magic not only ends Stoneskin, but any other spells cast on the target as well.

The Dispel Magic spell states:

Choose one creature, object, or magical effect within range. Any spell of 3rd level or lower on the target ends. For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell’s level. On a successful check, the spell ends.

Emphasis mine.

In your game, your Wizard targeted the BBEG with Dispel Magic. By the RAW, not only would casting Dispel Magic end Stoneskin, it would also end any other spells on the BBEG, regardless of who cast the spell or whether or not concentration is required. Because Stoneskin is a 4th level spell, the caster of Dispel Magic would need to make a DC 14 (10 + Stoneskin's level) ability check with their spellcasting ability to end the spell, unless they cast Dispel Magic using a spell slot of 4th level or higher.

If there were multiple spells of higher level cast on the BBEG, the caster of Dispel Magic makes an ability check for each one. Any spell on the BBEG of a level equal to or lower than the slot used to cast Dispel Magic ends immediately, no ability check required.