A large body of authoritative opinion has good reason to assume that their genes, together with inherited and acquired learning, have adapted them to the chase. Stress is a physical condition. Suffering is a mental condition. The former does not inevitably cause the latter. A marathon runner is highly stressed but is not suffering unless his stress exceeds anything that he has experienced previously and has not, therefore, mentally adapted himself to cope with.
Stress produces adrenalin and endorphins which produce exhilaration to mask some of the stress.
Also other tactics too numerous to discuss here. They use these tactics methodically while being chased. Foxes have been seen to kill and eat a small mammal while being hunted. For more details from Barnard and Hurst's work please click here. Certainly it is unproved and it would not stand up to legal examination.