I worked at Apple years ago and nothing was in my contract to say that I couldn't work for another company.

It is naive to think one can work at both companies simultaneously without repercussions if the manager(s) find out. The managers would not allow an employee to have a badge to the premises and access to the employees' email system at both companies. It would be legitimate grounds for termination. The employee can't sue for wrongful termination because the concepts of "protecting proprietary information", "trade secrets" etc are well-tested and upheld in court.

An employee can certainly resign (or get fired) from one company and then work for the other company but it is unrealistic to say those companies would allow concurrent employee relationships.