They don't have Canadian payroll set up and don't want to hire contractors.
Really, there is nothing about a TN that prevents you from working in Canada, because you don't need any authorization for you to work in Canada (as a citizen).
But what you are suggesting sounds wrong. Do you plan on paying US taxes but not live there? Do you plan on not paying Canadian taxes?
If you are getting a TN to prevent your employer from having to follow appropriate processes for employing people in Canada it feels like you are putting yourself personally at risk for this employer.
Again, I am not an attorney, but you should probably talk to one about options here because something just _feels_ incorrect about this set up.
Edit: I accidently remoted a sentence:
There are many organizations (PEOs) that try to solve this problem, such as https://remote.com/
If they're not in the US though (as a Canadian), they're not a resident, and therefore not a "foreign resident".
The entire situation is weird because as we both mentioned elsewhere, the correct approach here is a PEO (or setting up the appropriate hiring organization in Canada), rather than claiming to live (or work) in the US in order to get a TN (either or which would subject them to US taxation), and then claim to not when it comes to taxes.
What they can do is either a) have the US employer set up a Canadian subsidiary that handles their payroll or b) set up their own Canadian legal entity (corporation, sole trader??) and execute a services contract between the two companies. Then they can pay themselves under Canadian rules out of that company, or do whatever plumbers do in Canada -- sole trader or whatnot.
ianal, nor Canadian.
There are plenty of PEOs that will solve this problem. There's an entire well known legal pathway for this exact scenario.
Trinet is popular for instance.