They are correct. As a vendor your employer is responsible in your training for LOTO. You are responsible for the LOTO of equipment you are working on. OSHA states that employers of vendors and the company you are working at should compare LOTO procedures so there are no misunderstandings. You should always use your own tags and locks when working on equipment. The company you are working at may also require that their maintenance person also attach a tag and lock. I have ran into this same problem at numerous customers.