Yes. I would consider it unwise to use my own emergency funds to take care of someone else's emergency situation (unless they were a direct family member under which I had already taken financial responsibility), even though reserve funds might be able to be used for that level of problem situation of someone else .. such as a friend or a more distant relative who should already have their own emergency fund practices...
It'll indeed be unwise to use one's emergency funds (meant for his own personal emergencies only) to cover another person's emergency situation, as this coulf compromise and affect one's financial security and stability, except of course they are emergencies of direcr family members which could also be considered to be your own emergency too.
Your emergency should come first, as well as your financial well being, that boundary between your emergency fund and others' financial needs should be maintained and very clear.
It is a personality thing and I will not blame anyone who does that because such might just being doing that with a bid to finding peace within himself or herself. There are people that are so softhearted to the point that they can actually dip hands into their emergency funds to help someone they don't even know but need urgent attention. I have such a person which is my mum, who can inconvenience herself to please others. Her love for humanity knows no limit and because of her I feel some people are just born that way and there nothing that can change them.