Deoiling would leave even a higher pH than the coolant, and make it tougher for the acid to be efficacious. So the prescribed coolant treatment sequence can't be for that reason.

I often acid-treat metals in the lab. This is followed by a neutralizing treatment, accomplished with dilute ammonium hydroxide. When I run out of ammonium hydroxide, I use simple soap. If I do nothing, the metals continues to rust, no matter how many times I've rinsed the part with water.