Because of the construction of tyres, its impossible to assess the condition of the internal internal structure just by looking. So there is always a risk a second hand/ part worn tyre may have some invisible weakness. So that is a matter that you have to come to your own decision about.
But if your own car has been driven by someone else who knows what they may have driven over or up. I am certain there are some perfectly serviceable part worn tyres out there,
The National Tyre Distributors Association, (NTDA) website may offer some insight, but having read some of it, clearly there is an on going problem with unscrupulous rogue traders selling potentially dangerous part worn tyres.
About the NTDA Do you need a voice in the industry? Or an industry voice that can help you?The National Tyre Distributors Association, (NTDA), offers you
www.ntda.co.uk
How can the public tell the difference?
So that is a matter that you have to come to your own decision about.