Hello, welcome to the website. My name isXXXXX can assist you with this.
This depends on what you mean by "take on" one of the employees.
It sounds like you're being asked to engage that person directly, so you become responsible for their wages/tax etc.
What exactly did they ask you to do this with respect to this person?
If they gave you the impression you were just having him tag along to help out because they had no work for their employee, then I would argue that is a good indication that they were paying for him, after all, he is employed by them and you don't dismiss then re-employ somebody the next day etc. just because there is a one day lull in work.
So base based on that I would agree with you that it looks like you should be able to say that they remain responsible for his wages.
You could seek to claim the payment back, via issue proceedings against them in the small claims court (www.moneyclaim.gov.uk - where you can issue online). I doubt this will do much for your relationship with them as people to work with, but that's a decision for you.