I have not heard of any overseas company involved in this, but there is a lot of activity by a UK company which attempts to recover what they say are civil costs incurred as a result of shoplifting. I think this was the same sort of thing - not, as Eddie says, the police costs.
What is argued is that the shop's own security staff costs, & other staff & admin costs which arise from the shoplifting event, should be paid. However there was a recent Court case which threw out the claim - mainly because all the costs claimed were incurred by the shop anyway, whether the actual shoplifting event had occurred or not.
This probably doesn't set a precedent but anyone who gets this sort of worrying demand (often for around £130+) should not pay up but consult a solicitor or advisory service such as CAB. The CAB national body has done research & other work on this.