Would the plant and animal remains that it is said produces oil have migrated miles into the Earth? Is it likely?
It's marine plankton remains, mostly diatoms, to be precise.
And they don't "migrate" into the earth. They're deposited at the bottom of oceans and large lakes, and have sediments dumped on top of them over tens of millions of years. They're laid down and then stuff ends up on top of them.
You can find fossils of sea shells at the tops of some 12,000-foot peaks in the Canadian Rockies, so I guess it's not out of the question.