Being laid off is not considered a distributable event, correct? How do determine if someone who is "laid off" actually has a "severance from employment" so they can take a distribution from their 401(k) plan? The document does not reference the term laid off.

If the employee/employer relationship is severed, there is a severance from employment. If the person is free to find employment elsewhere I don't think the term used for the termination is relevant. It is a facts and circumstances test.

It could be defined in the plan document, but probably not, in which case the PA should look to employment definitions in personnel policies. If a collective bargaining agreement is relevant, look there first.