And not getting out of bed in the morning is the safest.
It’s never pleasant to crash a bike. Any bike. From your description, I’d guess your physician fell over sideways and landed on his shoulder rather than on his head by going over the bars. If he had gone ‘over the bars’ the injuries would have been skull fracture and/or cervical fracture(s). Clavicle fracture(s) would have been a secondary concern. Had he fractured his skull and/or broken his neck, he would likely be permanently disabled or paralized. So, yes, riding a bike is more dangerous than not.
So is getting out of bed in morning. Every morning. Driving a car is even more dangerous, by a factor of more than 38:1 (yes, I can cite sources for those numbers). But I bet you do it without thinking about it. amIright?
And you know what? He was right about injuring yourself running on a treadmill. No, it doesn’t happen all at once in a catastrophic accident. It happens slowly over time as you gradually pound your joints into mush. At least cycling is low impact and doesn’t stress your spine and joints.
One of the good things about riding a recumbent is that if you drop the bike you take the impact with your feet, your butt or your thighs primarily. Not your head, not your neck, not your shoulders, not your ribs. Leaving skin on the pavement is painful, but it beats a fractured skull and/or broken neck any day.