In solid form the risk is mitigated because there isn't enough surface area for the reaction with oxygen, it's the powder/shavings that are a concern. You can actually weld magnesium parts without it igniting.
Reading up on it a little more - it seems with enough heat solid magnesium can start a self-sustaining burn without oxygen. I wish I could find a laymans explanation of the difference between oxygen fueled magnesium powder fire and self sustaining. Must take an awful lot of heat if a welding arc isn't hot enough to cause this.
Edit: Also think of steel wool and how well it burns, but a block of steel not so much.