You keep posting this article, but it has no evidence in it. It links to several papers that tangentially support your claim. Let's look at a different paper that somewhat refutes it:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4032801/

Here's the raw data on prescriptions and outcomes summarized in that paper, built from claims data for 2000–2005:

  Opioid Dose and Days Supply
                         total       addiction
  No opioid use          371,371     150 (0.04%)
  Low dose, acute        90,415      111 (0.12%)
  Low dose, chronic      6,902       50 (0.72%)
  Medium dose, acute     83,542      101 (0.12%)
  Medium dose, chronic   3,654       47 (1.3%)
  High dose, acute       12,378      15 (0.12%)
  High dose, chronic     378         23 (6%)

So acute opioid doses 3x your risk of addiction, no matter the strength. And long term dosing will 18x to 150x your risk, depending on the strength. Relatively few people are receiving chronic (90+ days) opioid doses, but those that are have a significant risk of addiction.

I'm not the right person to do this analysis properly, but I'd hardly call this "thoroughly debunked"

And yet the CDC notes that your likelihood of developing opioid use disorder rises precipitously after as little as five days on prescription opioids. https://www.cdc.gov/mmwr/volumes/66/wr/mm6610a1.htm

Regardless of whether or not this accounts for the majority of addictions, it is sufficient to say that opioids are far more dangerous for patients than many doctors believe. Addressing prescribing habits is a necessary part of a multi-pronged solution to opioid addiction.

What is the predominant mechanism of becoming addicted then?

"Far greater risk comes from simply being young and from using alcohol and other recreational drugs heavily. Ninety percent of all drug addictions start in the teens — and 75 percent of prescription opioid misuse begins when (mainly young) people get pills from friends, family or dealers — not doctors. Opioids are rarely the first drug people misuse."

All that tells is that there is a layer a indirection. The friends, family, and dealers to some degree get pills from people that got them from doctors. Some may come from overseas, theft, etc., but if 25% are hooked directly from having been prescribed them, I would guess a big portion of the 75% is people within a few hops away.

Often what happens is that the 25% that got hooked from being prescribed start buying additional pills. Eventually they can't afford that and they switch to cheaper heroin, often funded by selling their prescription pills.

You could still draw a link: high prescription rates of opioid pain killers normalises the use of them and as such someone is more likely to be offered them by family and friends for something minor.

Also, is “throughly” debunked really the case? That makes it sound like there can be no link at all, but higher levels of these in society legally could lead to an increase in abuse. On complex topics like this it is rarely possible to talk in absolutes.

What's debunked is the very common narrative in this thread that poor Uncle Billy went to the doctor with a bad back and came back a rabid addict. Non addicts becoming addicts from regular prescriptions is very rare according to all studies.

There is definitely a big complex drug ecosystem otherwise, though.

I followed these links last night and didn't find much support for that statement. If you're going to quote something, how about the paper?