To me, it matters to a certain degree. In theory, quality control should be dependent upon the company. But I've seen evidence to suggest otherwise. Just look at Mattel and their toys sourced from China. A country with a sub-par reputation for quality control would be crossed off my list, regardless of who the manufacturer is.
The other time country of origin would matter to me is in an entirely different situation. If I were to cross the border and buy my tires in the USA, put them in my trunk and drive home to Canada, then country of origin matters from the perspective of duty I would need to pay at the border. I would prefer a NAFTA country made tire, as these get 0% duty - only attracting sales/eco taxes. Sourced elsewhere, and there is duty.
To date, I've used tires on my own vehicles (OEM and replacement) sourced from Japan, Korea, Canada, USA, Brazil and Germany and have no complaints that could be associated with quality control/safety (performance is another issue, but that has to do more with brand and model). My trailer however has Chinese tires, and I can't say I'm impressed or even confident with them. Wear is quite uneven, and mileage on them isn't that high. Possible it has to do with alignment, which would not be the tires' fault, but unless alignment were grossly out, which would then be otherwise noticeable while towing, there's no way they should have such pronouced feathered edge wear for so few miles, unless there were quality issues. Thankfully, this particular brand, one of two that are sourced from China for trailer tires, does not seem to have a disproportionate number of catastrophic failures (blowouts, tread separation, etc) based on internet searches.