Well,we all look at things differently,but one thing that does not differ,an animal sick or wounded needs a vet.
The fact is,as Lucky mentioned,purring can mean a lot of things,even pain..
Your story of a rescued kitten would have been heartwarming had you not used the wording"flattened head"bloody nose and mouth.I felt good when you said you wrapped him in a blanket,thinking you brought him to a vet,but then you just put him in a box
We are all animal-lovers here and the idea of a kitten with a flattened head,made me a little sick
Animals,unlike us,deal with pain and injury in a different way,they just adapt to whatever they are dealt.
This kitten could have a cracked skull or other severe injuries and still purr.
I am glad you look after your dog exemplary,but does a defenceless little kitten not deserve the same care??
And yes,you are responsible for ALL animals in your care,including farm-cats,no animal should suffer needless pain....as for wounded birds or mice,I would not take them to the vet,but would certainly end their suffering one way or the other.