Those numbers "about half of all software engineers have a degree" [wikipedia]. "Nearly half of the software developers in the United States do not have a college degree. Many never even graduated from high school" I haven't been able to find a single study that confirms those statements, and it isn't corroborated by my own experience. Even if they were real, what would they even mean?
If all people who write programs of all type are included, the number may have some validity, but in my team which builds software that runs an advertising network 6 of the 8 software enigneers have a degree. The two outliers are a developer with twenty years experience building software, and a senior graphic designer who is holding an internship level software engineering position because the company wanted to support his desire to change careers. Across the engineering department, a hand full of engineers have degrees which aren't computer science, but very few of them have no degree at all.
Building software is a lot like other skills, skill sets vary. You don't hire a detailer who you pay $20/hr to wash cars to paint a car if you want car-show quality results; you hire an auto-body expert and pay him $100/hr. Similarly, you might hire any old contractor to build a garage, but you don't hire any old contractor to build you a thirty story building — you hire a real architect, and a real engineer. On the same note, you can't hire someone who just "can program" to build a system that runs a business of much scale.