The relevant question is who holds the professional employment relationship, not who processes payroll. Where an outside organisation only administers pay and benefits while the operating company assigns and directs the work, the operating company is the one that must describe the position.
Look past the pay statement
A co-employment arrangement can allocate responsibilities among several parties. Ask which entity directs duties, pays, owns the work product and can end the assignment, then give counsel the actual agreements. Those facts help identify the relevant relationship for the chosen route.
A pay statement name alone does not settle the answer. Order matters more than volume here. Settle the direction question before the paperwork question: an operating company that cannot say who assigned last month's work is not yet ready to describe the position in a letter.
Two conditions never move with the payroll structure and are worth confirming first, because a negative answer ends the inquiry before any agreement is read. The position must fall within a profession listed in the USMCA appendix, and the applicant must meet that profession's own qualification requirement, which is not satisfied by comparable experience unless the listed entry says so. The principal must also be a Canadian or Mexican citizen; permanent residence in Canada does not substitute.
Self-employment is not permitted, so disclose any ownership interest in the operating company at the outset rather than after documents are drafted.