I never even realized that this existed in the Park, but given the restrictions there are only a few instances where it makes sense for fishing. It probably makes more sense in other parks (like RMNP) without the network of trails, etc...
(from the Park Compendium
Camping in the backcountry is permitted only at established backcountry sites, except as authorized by a cross-country permit. Cross-country permits may not be self-issued and must be approved by a Resource and Visitor Protection Division employee. Cross-country camping (at other than designated sites) is permitted under the following conditions:
- The maximum party size is four persons. The use of horses or other stock is prohibited.
- The campsite must be at least one-half mile from any designated trail, one mile from any designated road and 100 feet from the nearest surface water.
- Camping in spruce-fir, beech gaps or on grassy or heath balds is prohibited.
- The duration of stay at each location cannot exceed one night and the same location cannot be used a second time on the same trip.
- Wood fires are prohibited.
- Campers are required to obliterate all traces of human presence upon leaving a cross-country camp.
- Camping locations for each night should be as closely pinpointed as possible using natural landmarks or map coordinates and so noted on the permit. Trips are expected to follow the designated itinerary as closely as possible.
Cross-country hiking is a special use and requires special equipment, training and/or experience. These regulations are an attempt to permit this special use, while minimizing the potential impact on natural resources.
(b)(3) Camping within 100 feet of a flowing stream, river or body of water is permitted only at designated front and backcountry campsites.
I can see that it would make sense if you fished one of the upper tributaries of streams like Hazel, Deep Creek, Fish Camp Prong, etc...It would have to be a half mile up the a tributary (to be away from a trail) and more than 100 feet from the stream...