If I outsource work to others, am I responsible for their tax and NI?

I am a self-employed freelancer. I outsource work to people on sites such as fiverr.com and other freelance sites. One of the things I do is I pay somebody to place classified ads on free classified ad sites (such as Backpage.com, Gumtree, etc) so I can promote my services. For example, I pay somebody $5 to place 50 ads on backpage for me.

Now, I was talking to a friend of mine today and he said that legally I have to ensure that the people I am outsourcing the work to must be self-employed, and that I am responsible for their tax and national insurance, and that I must check up to see whether they are self-employed, otherwise I could get in trouble. Is this true? Surely the person who I outsource the work to is responsible for their own taxes, and it is nothing to do with me? They are not employed by me...they're self-employed and just someone I hire.

If I outsource work to someone, e.g. if I pay someone to places ads for me, then the money I pay them is a tax-deductable expense for me, right? It is an EXPENSE for me, but an INCOME for the person I hire, therefore I'm not responsible for their tax or NI?

Also, most of the people I outsource work to are in the USA, India, and other countries. I am in the UK. How does all this tax stuff work internationally?

Thanks for your advice.