Sure it wasn't exactly foul play, but it was a major legal exploit that has since been patched. If the exploit didn't exist in the first place, then Amazon probably wouldn't either.
Outside of math, science, and law, proof and evidence are tricky words. Instead I merely offer a quote for your consideration, from Brad Stone's book The Everything Store (2013):
"""
Bezos chose to start his company in Seattle because of the city’s reputation as a technology hub and because the state of Washington had a relatively small population (compared to California, New York, and Texas), which meant that Amazon would have to collect state sales tax from only a minor percentage of customers…. [T]he University of Washington produced a steady stream of computer science graduates. Seattle was also close to one of the two big book distributors: Ingram had a warehouse a six-hour drive away, in Roseburg, Oregon
"""
In other words, Bezos was well aware of the sales tax advantage from the start.
I mean, it was settled law from 1992. Certainly, SCOTUS ruled differently in 2018, and SCOTUS rulings aren't always moral or fair, but nobody is going to pay a tax if there's case law that says they don't have to.
Better prices wasn't the only reason for Amazon's sucess. A wider catalog was also a big deal, and paying sales taxes wouldn't have impacted the size of the catalog. Afaik, they also did well in states where they had nexus and paid sales taxes from early on, too.
Amazon started as a bookstore and famously didn't see profit for years. The larger catalog didn't come into play until after the business model and technology were battle tested. Yes the catalog helped by triggering their hyper growth, but they were well established by that point.
It had a larger catalog for books too. Same process to buy current best seller and anything else in print. As opposed to going to the book store and if it's not there you've got to find someone who can order it, and then it arrives at the store and not your house.