In my (totally unprofessional) opinion, C25K progresses too quickly for most people. It think the "None to Run" variant is better (and emphasizes that repeating weeks is normal, and even expected)
Few years later I'm a softbody IT guy looking to shape up, and decided to follow the reddit C25K sub -- it killed my shins. Bad splints, had to cut out running for a while. I got there eventually but I think 60 minutes of biking or eliptical + leg workouts did more for me than the C25K (as written) did.
As a general comment, shin splints is the classic beginners too-much-too-soon running injury. Experienced runners get a whole range of other injuries, but rarely shin splints. The only time is after they take a break and try and come back too quickly (notice the pattern).
By running slowly a lot, your body has time to learn how to run efficiently and safely simply by trial and error. By not overdoing it, you give your body time to recover from any errors made during the "trials", without injury.
Incidentally, lot of slow running is also a great way to build up base endurance, so it is not wasted time, and you will "recoup the investment" later, when you start running longer distances.
Shin splints suck, though. Even experienced runners get them from time to time. Probably best to switch it up a bit, include swimming or bicycle instead of some runs every now and then.