Jim Macklin wrote:

Right of way DOES NOT mean carte blanche, see
2-1-1. ATC SERVICE

The primary purpose of the ATC system is to prevent a
collision between aircraft operating in the system and to
organize and expedite the flow of traffic. In addition to
its primary function, the ATC system has the capability to
provide (with certain limitations) additional services. The
ability to provide additional services is limited by many
factors, such as the volume of traffic, frequency
congestion, quality of radar, controller workload, higher
priority duties, and the pure physical inability to scan and
detect those situations that fall in this category. It is
recognized that these services cannot be provided in cases
in which the provision of services is precluded by the above
factors. Consistent with the aforementioned conditions,
controllers shall provide additional service procedures to
the extent permitted by higher priority duties and other
circumstances. The provision of additional services is not
optional on the part of the controller, but rather is
required when the work situation permits. Provide air
traffic control service in accordance with the procedures
and minima in this order except when:



No document I have found says that declaring EMERGENCY means
ATC shall grant any pilot request, those requests have
limitations due to traffic and other events. Right of way
and priority handling does not mean that every PIC request,
demand or wish can, will or should be granted.

Handling a flight with an emergency isn't an "additional service" as
defined here. This is talking about optional services like VFR
advisories, not dealing with an emergency.

Matt