This claim is repeated over and over as evidence that wolves and therefore dogs are omnivores. However, this assumption is just that--an assumption. It is not supported by the evidence available to us, and is therefore false!
Wolves do NOT eat the stomach contents of their prey. Only if the prey is small enough (like the size of a rabbit) will they eat the stomach contents, which just happen to get consumed along with the entire animal. Otherwise, wolves will shake out the stomach contents of their large herbivorous prey before sometimes eating the stomach wall. The following quotations are taken from L. David Mech's 2003 book Wolves: Behavior, Ecology, and Conservation. Mech (and the others who contributed to this book) is considered the world's leading wolf biologist, and this book is a compilation of 350 collective years of research, experiments, and careful field observations. These quotes are taken from chapter 4, The Wolf as a Carnivore.
This next quote can be found on the Hunting and Meals page at Kerwood Wildlife Education Center.
From the mouths of the wolf experts themselves, who have observed countless numbers of kills: wolves do NOT eat the stomach contents of their large prey, and are carnivorous animals. Additionally, Neville Buck from the Howletts and Port Lympne Zoological Parks in Kent, England, notes that virtually no small carnivore (which includes varieties of cats, wolves, wild dogs) eat the intestinal contents of their large prey. The contents are spilled in the enclosures and are often rolled in by the animals, but very little is eaten (if any is eaten at all). His observations can be found in Appendix B of Raw Meaty Bones.