I don't know if machines are necessarily 'safer.' For the guy/gal who just walks in off the street never having seen a weight lifted, maybe. But machines can also put folks through unnatural ROMs - esp. if their bodies aren't made for the machine (like short women).
Many people have back problems (walking upright makes humans prone to back and knee problems), but I don't see how lifting free weights with good form (and good sense) could CAUSE back problems. If anything, well-executed compound moves with free weights could help to stabilize a person's back (and anything else).
I have a troublesome lower back, and I use dbs, bbs and cables (for pull-throughs, rows and standing abs) 95% of the time. I've worked out with 100% machines before (because that's how they steer the ladies) and this way, and this way is MUCH better in terms of results. I'm now using a Gravitron assisted chin-up machine to help me learn how to do chins until I'm strong enough to do the "starter" exercises (like negatives) without the machine.