Utah Supreme Court has ruled

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your interpertation is pretty likely.
Example:

You will be able to start at the road where Thousand Acres Ranch and Smith-Morehouse road split and be able to walk upstream to fish. You may not drive up the road, get out and TRESSPASS to get to the river, then fish.
You must walk up the river from the public access and you must return down the river to public land to get out.
The only private property that may be touched is the streambed. You may leave the streambed only to get around obstructions and then only in the least impacting way to the land owner.
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