Well, your basic idea is correct (bigfoot is a modern story with no real connections to past traditions), but the history of bigfoot certainly is more complicated than you said. It really started in the late 1950s, spurred on by the Wallace hoaxes and the public interest in the Himalayan Abominable Snowman (itself a western misinterpretation of local legends). Basically, Wallace hoaxed tracks, people started talking about an Abominable Snowman in America, and all of a sudden bigfoot happened. It has a little bit of precedence in stories influenced by the European wildman tradition (ex: Jacko); although most of those stories weren't linked until the late 50s, they provided a background for the character of bigfoot to exist, mostly through ideas of savages/noble savages and people misunderstanding paleontology (ape-men lived in the past, so ape-men could be running around now). A for Patterson's role, I'm not sure it was quite that big. Yes, the PGF was huge and boosted the public's knowledge of bigfoot, but Patterson was coming into an already existing field and did very little that others had done, besides make that film. As far as I know, most of what he did was just copy other people's (mostly John Green) work; his film was hugely influential and is probably the main reason the public started to believe as heavily, but he wasn't personally responsible for a lot of "research" as far as I know.
The Native American part is completely disjointed from that development. I actually couldn't find out when people started linking them together (I think John Green's stuff from the early 60s is probably when it started), but they're not related at all. The two traditions talk about different things and they serve different purposes (not to mention how different many of the Native wildman stories are from each other). Even when JW Burns published the stories that led him to invent the word "Sasquatch," he did it as a presentation of superstitious Indian stories, not as valid folklore or accounts of phenomena. The two seemingly only became linked as an afterthought because someone, likely John Green, thought it lent his stories credibility. Suttles, in his article, actually calls Green out by name and frames his analysis at answering some of Green's criticisms.
Or at least, that's the basic gist of what my research led me to conclude. I don't want to sound like a know-it-all or to be argumentative, I've just done a lot of research on the subject and want to state what I know. Bigfooters lie about their history/tradition, and I think it's important to call them out on that. Not only is it dishonest, but it's also incredibly disrespectful to the Native traditions they're appropriating and misrepresenting (my paper was for a Native American religion class, so most of my research went towards that). A lot of people have written about all the bad science behind bigfootery, but I think presenting the legend as a modern invention does a lot to hamper its credibility, too. I'm actually surprised so few people have approached it from that angle.