They are unusual to be sure, but Baker Mayfield isn't a sole exception (ignoring for a moment Otto, who does really count). A few others:
Former Washington Redskin QB Colt Brennan was a walk-on QB from Hawaii who set record upon record in the NCAA. The most impressive one is his mark for consecutive games with 200 or more passing yards. He set that mark at 34, and he played only 38 games for the Warriors. He had a career completion percentage over 70, and he was an All-American once and an All-MWC selection twice. Brennan capped his college days off as a sixth-round pick in the 2008 NFL draft.
Another Hawaii QB, Bryant Moniz was a walk-on and a 3 year starter. In the fourth game of the 2011 season, Moniz tied an NCAA record by throwing seven touchdown passes in the first half in a 56–14 victory over UC Davis. Moniz finished his career with 10,169 passing yards and 75 passing touchdowns in just three seasons, both of which are third in school history, after Brennan and Timmy Chang.
Jonathan Smith who is the new head coach at Oregon State was a walk-on QB there who came in during the middle of his freshman year (with no scholarship) to lead the Beavers. Ended up a 4 year starter and as a junior, he led the Beavers to their greatest season in school history in 2001. The Beavers finished 11–1–a school record for wins, won a share of their first conference title in 36 years, and finished fourth in the country. Smith was the MVP of the Fiesta Bowl.
And then you have to also consider the plethora of great FCS/Division II QBs that went on to star in the League. Like Jimmy Garropolo (Eastern Illinois), Steve McNair (Alcorn State), Rich Gannon (Delaware) and Kurt Warner (Northern Iowa), Tony Romo (Eastern Illinois), Ryan Fitzpatrick (Harvard), Josh McCown (Sam Houston State). When Joe Flacco (Delaware) stepped onto Ryan Field, he was the best QB on either sideline much to our dismay. None of these guys had Division I offers (well, I'm guessing none, since they ended up in FCS) either, and could have opted to walk on instead at a FBS school like Green (who spurned a scholarship offer at FCS N. Dakota State). And all of them would have won the starting job at NU regardless of what year they played here since perhaps Otto Graham. Every year there are multiple FCS QBs taken in the draft. In fact, in a given year, there are multiple starters and a dozen or so FCS QBs on NFL rosters:
https://herosports.com/collegefootball/yes-mr-qb-you-can-make-the-nfl-from-the-fcs/
All of a sudden, the pool of great QBs who were overlooked by the big schools and not given scholarship offers, but could have starred anywhere, is much bigger than just Baker Mayfield.
I think you have to look past the statistics when you look at individual cases, just as you do when you look at no star and 2 star recruits. If a kid is special and is just being overlooked for some reason, the stars and even the scholie doesn't matter. In this case, if Green was as tall as he is now in HS, he would have gotten plenty of scholarships, at least according to his coach, who also coached Nathan Scheelhaase, who was a unanimous 4 star recruit, 4 year starter for the Iollini, and holds the Iollini record for offensive yards. Rockhurst's coach said that Scheelhaase was not nearly as skilled as Green, just bigger. Interestingly, Green is now the same 6'2" that Scheelhaase was as a HS senior.
You look at TJ Green's body of work as a HS Senior, his awards, his skill set, his heart, not to mention the bloodlines, you look at also the reasons he was overlooked - in term of his size and how he's grown a couple of inches since, and then you also consider that he is the QB that is highest on our depth chart who is healthy and returning (though of course we don't know where Marty would have been had he had not redshirted) and the prospect of him competing for the job and even winning it is not at all far fetched.
I for one am higher on his projected ceiling than I am of Jason Whittaker, just solely based on HS level production. Whittaker may have a higher absolute ceiling, but he's clearly a project. QB is a position where intangibles are as important or even more so than physical attributes, as the Siemian vs. Lynch saga attests.
FWIW, I think the position is up for grabs, and if you forced me to guess who wins I'd pick Marty (love his film - though it's easy to love everyone's highlight films - and his production in HS was impressive), but I think TJ is his main competition and will give him a run. I think Smith is behind, and Whittaker has no chance as a project and true frosh.