Fill can suffocate roots of oaks.
Yes, burying live oak trees and their roots under fill during lot leveling can definitely harm or kill the trees. 4 feet is a lot of fill. Placing it against the trunk can put the trunk at risk of tissue death and infection.
As trees grow, they develop root systems in the soil. Many of these roots are in the upper foot of the soil because this is where water enters the soil, where nutrient availability is highest, and, importantly, where oxygen availability is highest. Roots breathe oxygen, and oxygen diffuses slowly through the soil, often travelling through voids in the soil created by burrowing organisms or left after decay of roots.
To bring heavy equipment into this root zone is to compact and destroy these air voids. To put fill onto this is to bury them. It may be the buildup of toxic gases, rather than the lack of oxygen, which then kills the roots. Significant root mortality is likely, possibly resulting in visible reduction in vigor and perhaps death. Larger, older trees are in an especially delicate balance with their environment, and are especially susceptible to decline and death due to environmental change.
To understand a tree, picture yourself standing waist deep in water. Only your upper half is visible. Now imagine a shark eating your invisible half. Your visible half looks great. How do you feel? How long will you remain standing? Trees can stand for centuries, but only if they have feet to stand on.
The root zone of a tree radiates out from the tree, often well beyond the extent of the overhead canopy of the tree. Without seeing your trees, I cannot tell you how large of an area you need to protect from this grading you intend to perform. I suggest you hire a competent arborist.
If your arborist recommends putting ventilated pipes on the ground and putting that 4 feet of fill on top of it in the root zone of the trees, you might consider hiring a different arborist. Such a system is no substitute for the air/soil interface, and soil void network your trees have grown in to date.