Are the brains of any herbivorous animals capable of utilising ketone bodies as an energy source?
My answer is limited to sheep.
Background
The metabolites referred to as ketone bodies (which I will refer to as ketones from now on) are acetoacetate and β-hydroxybutyrate. In humans these are produced in the liver when the amount of acetoacetyl CoA being produced exceeds the capacity of the TCA cycle. These acetyl groups are instead used to produce acetoacetate, and this can be reduced to β-hydroxybutyrate.
The production of significant amounts of ketones occurs during fasting (diabetic ketosis will not be considered here). Once glycogen has run out, the bodies requirement for glucose has to be met by gluconeogenesis (mainly in the liver) - glucose is synthesised from various carbon skeletons including glycerol and the products of amino acid catabolism (coming from muscle protein turnover). This means that in the liver the function of the TCA cycle shifts almost entirely to supplying oxaloacetate for gluconeogenesis, via the activity of phosphoenolpyruvate carboxykinase. Thus there is no oxaloacetate available for citrate synthase, so acetyl CoA cannot enter the TCA cycle. However, because fasting also results in fat mobilisation the level of acetyl CoA in liver cells goes up (acetyl CoA is the end product of fatty acid breakdown).
So what is going on here? During fasting the fuel economy of the body has to switch from being heavily glucose-based to one which uses carbon from fat and from protein. The ketones are the manifestation of this, and many tissues become heavy users of ketones during fasting as blood levels rise to 5 mM within a few days. This means that the glucose being produced by the liver can be directed towards tissues which are more dependent upon glucose. The classic example of such a tissue is the brain, but in humans even the brain begins to use ketones heavily during fasting.
In ruminants the situation is entirely different. Ruminants rely upon the bacteria in the rumen to metabolise carbohydrate in their diet and this results in large amounts of alimentary ketones entering the blood directly. For their glucose supply ruminants rely entirely upon gluconeogenesis, and the substrate for this is propionate, another end product of bacterial metabolism in the rumen: a lactating dairy cow will synthesise over 3 kg of glucose per day.
So, when I read this question my reaction was that the statement must be incorrect - surely it would make sense for sheep to use ketones in all tissues. However my intuition was wrong - according to

Pell JM.&amp; Bergmane N(1983) Cerebral metabolism of amino acids and glucose in fed and fasted sheep. Am. J. Physiol. 244: E282-E289

cited in

Heitmann RN et al. (1987) Hepatic ketogenesis and peripheral ketone body utilization in the ruminant. J. Nutrition 117: 1174-1180
&quot;Although there is some oxidation of ketone bodies by the brain tissues of humans and rats during prolonged fasting, Pell and Bergman ,using an elegant in vivo preparation, have shown no significant uptake or oxidation of ketone bodies by sheep brain.&quot;

I don't have access to the Pell &amp; Bergmane paper so I cannot explain what they actually did. What is clear from the review by Heitmann et al. however is that fasting ruminants respond in the same way that we do, switching to hepatic ketogenesis, and presumably they also maintain gluconeogenesis, using not propionate, but amino acid carbon skeletons. The context of the statement quoted above suggests that even in the fasted state the sheep brain doesn't use ketones.