Squealer's account of Boxer's death is not believable in Animal Farm because we know that he did not actually go to the hospital.
When Boxer is too injured to work, a truck comes to carry him away. The other animals read on the side of the truck that it is from the knacker's, where Boxer will be killed and made into glue or dog food.
Squealer suggests that Boxer died peacefully in the hospital, and he was at his bedside.
And at the end, almost too weak to speak, he whispered in my ear that his sole sorrow was to have passed on before the windmill was finished. 'Forward, comrades!' he whispered. 'Forward in the name of the Rebellion. Long live Animal Farm! Long live Comrade Napoleon! Napoleon is always right.' Those were his very last words, comrades.' (Ch 9)
The animals are told that the van was bought by a veterinary surgeon, and did not belong to the knacker’s at all. However, we know that Napoleon’s greed got the best of him. When Boxer was no longer able to work he simply became another income source and then a propaganda tool.
Squealer's story might have fooled some of the animals, but by now the smarter ones knew how he stretched the truth.