Revenue Quebec has faced many ITC claims for GST/QST based on third party invoices, often, as in this case, involving payments to temporary employment agencies. RQ finds or suspects that these third party agencies are not real businesses but shell companies that give "convenience bills" ("factures de complaisance") to allow the registrant to claim ITCs, in effect, on its own payroll.
In this case, Justice Lamarre believed the government's witnesses that the convenience companies (the pretend temporary employment agencies) didn't have or hire out the employees the registrant claimed it contracted for. And the temp agencies were known to have been involved in this kind of tax fraud in the past. (Para. 51)
Even so, the registrant claimed the temp agencies had found the workers and it used them, regardless of whether they were employees of the temp agencies. This claim doesn't really seem to make sense and Justice Lamarre didn't believe it. (Para. 54.)
The real story seems this: The registrant sought to lower its labor costs by using illegal immigrant workers, paying them less than market wages. At the same time, the registrant sought to avoid paying payroll taxes while also getting ITCs on its labor costs. The "temp agencies" were mere facilitators of the scheme; they had no employee; the workers were, in truth, employees of the registrant. And so, the Court agreed with Revenue Quebec that the registrant wasn't entitled to ITCs. (Employee services are not taxable supplies; employees don't charge GST and employers can't claim ITCs on the wages.)
See also: Pépinière A. Massé Inc. c. La Reine, 2014 CCI (Paris)
See Kosma-Kare Canada Inc. c. La Reine, (2014 CCI Lamarre) (But see Kosma-Kare Canada inc. c. Canada, 2014 CAF (Gauthier) (upholding the TCC on ITC disallowance but rejecting penalties and late reassessment.)