I think that's a bit of an underestimate. Short sleeves basically expose only the skin on the top of your arm from the elbow down. That's a lot less surface area compared to your full front and back, shoulders, and neck. Your chest/shoulders/upper back will also be receiving direct, unbroken sunlight, while your arms are probably blocked a good deal when they are at your side by shadows.
If it were that easy I don't think deficiency would be so prevalent. I agree that it's almost impossible not to get 30 min of partial exposure.
SPF means "sun protection factor". SPF 10 is not "completely exposed" it's actually a very high level of protection, it means that it will take 10x as much sun exposure to lead to the same amount of UV-B reaching your skin, more or less.
SPF 10 is 90% covered, and cotton T-shirts are usually higher than that. You'll find that you can see visible light through a T-shirt at around a 10× reduction too.
If it were that easy I don't think deficiency would be so prevalent. I agree that it's almost impossible not to get 30 min of partial exposure.