The corp is a subsidiary. It is irrelevant if and how long you worked there for, the parent company has the financial and legal control over all the subsidiaries. The foundation literally owns the corporation, no need for quotation marks. If they have not or do not exercise that control or interfere in the day-to-day life today, that does not mean they will not do it tomorrow or whenever it becomes necessary. When shit hits the fan all that matters is what's on the paper.

I can also say, that my hypothetical landlord has nothing to do with the place I have lived in for 10 years. So therefore they do not "own" it.