My apologies for the late reply.
So, when I landed, something went wrong (whether it was the officers fault, or a computer error, I don't know), and so the system did not know I had landed. That meant that the PR card process didn't get started. So when I went to get my SIN, I couldn't get it, because I wasn't in the system as a PR. After calling Immigration Canada multiple times, the second or third person I talked to, explained to me that there had been an error during my landing and that nothing had been set in motion.
So no, SIN and PR aren't directly linked, but if you aren't in the system as a Permanent Resident, it is obviously impossible to get your SIN.
I called customs in the city I had landed (Victoria,BC) and told them what happened. They told me I had to go back to a customs office and land (again). They made sure everything was ok, every button was clicked, and I had officially landed.
I went to Service Canada right after I had successfully landed (literally around the corner) and 20 minutes later I had my SIN.
My PR Card arrived about 8 weeks later, if I recall correctly.