I think that these kind of policies need to have a certain amount of "bend" to meet unique business-related situations.
One approach would be to require deviations to the published policy documented in permanent records, to be approved by a member of senior management, and (this is most important) for the business necessity of the request to then be "affirmed" by a second member of senior management (maybe the head of HR).
The idea here is to reinforce the concept that exceptions must be few and far between, and mot to be requested in a light manner. Knowing that even the Chairperson cannot bypass the process would let the general staff members that travel that the standard (non-emergencuy) policy has credibility.