Of course it is not true.

Q1: Olay used to call The Oil of Olay. That's why some people thing it has oil and not good for oily skin. To avoid the misleading, Olay deleted the "Oil" from its brand, and just uses Olay.

Q2: Of course it has nutrients like any other brands. You can check out their sites.

I have been using Olay's SPF 15 for years. I usually use one other product and switch back to it.