The simple answer is that everyone is different. Every article/blog/video on skincare out there will swear that you absolutely NEED to moisturize every-time you cleanse your skin. However, there are plenty of people out there that don't and are fine. I have heard all different responses from friends/family when I asked them about moisturizing: Not at all, only when they feel like it, only the parts of their skin that feel dry, only in the winter, only before make-up, etc. But the main feel I got from everyone was that they aren't strict with what they do, they just do what feels right and don't really worry about it.

So, I personally think that it all depends on you and your needs. The internet will always make you feel like you NEED to follow certain steps and routines, but that's honestly not true. Everyone is different, and everyone needs different things. There is no requirement.If you want to moisturize and it makes your skin feel good than do it. If you don't, then don't force yourself to because you think you need to.

It also depends on what else you use on your skin. If you use a lot of cleansers/toners/acne creams/make-up then I would personally suggest using one just to make sure your skin is not becoming stripped and dull. But if you never wear make-up and only wash your face with water or a gentle cleanser, then you have more freedom to decide what feels best.

Some people get oily skin when their EFAs (essential fatty acids) are out of balance.Most people get too much 6 from fast food and other sources from eating the American diet, and not enough 3 (from fatty fish like salmon and other sources). Our bodies make their own 9, but not everyone's produces enough for one reason or another.  This imbalance can stimulate the oil glands and lead to chronic oily skin. 

You could try taking hemp seed oil. This has a mix of all 3 EFA's (3,6, and 9). For some, it can help reduce oil excess oil production. It helped me a lot while I was taking it. I've since replaced with regular fish oil. But maybe I'll start incorporating it again, as I've been noticing oilier-than-normal skin as of late. Hadn't been a problem for a long time.

But to answer your question, those who don't deal with these imbalances generally don't have skin that's out of balance (too oily or too dry). So the need to moisturize becomes more a matter of personal preference or choice, like the above poster suggests.

Moisturizing even when oily can help send signals to oil glands to cool it..."we're all set, no more oil please." That's how I discovered that my problem wasn't just oil, it was very dehydrated skin! It's been better since I started moisturizing.  I do find I'm more apt to get oily later in the day if I forget to moisturize after showering. Then my oil glands get the opposite message..."uh oh dry skin! Oil to the rescue!" And I'm like, "Thanks guys, you shouldn't have have...really really shouldn't have...."