People with oily skins don't stop producing oil if they wear moisturizer. It doesn't work that way.
It's not dependent on what you put ON your skin. You can dry your skin out with certain topical ointments (medicinal ingredients) but emollients on the skin don't prevent the skin from producing more.
Nowadays, they sell moisturizers to all-skin types with SPF and that's why they come for people with oilier skin types. Gel based (oil free). I wear one for combination skin.
Sometimes it also helps for going under makeup, etc.
My teens skip moisturizer. They have no need.
*I was sold the clinique 1-2-3 system at age 16 and most skin care regimes come with a cleanser, toner and moisturizer or protector (is how they sometimes market it). That can be considered any barrier .. gel/sunscreen/balm.. whatever. The toner is supposed to replenish your skin's Ph balance after your cleanser (I don't know if this is true) because the cleanser strips your natural oils. it also removes the last traces of cleanser/soap and residue (possibly left over makeup). Technically, you can skip this. I was told same with moisturizer, UNLESS you feel tight after the cleansing say, 20 minutes afterwards. That's how you know if you need one.