It's been quite some time since I rolled the numbers, but as I recall the majority of radiation exposure at high altitude is not X-rays, but cosmic radiation - high energy stuff.

There's a break-even point on shielding, given that secondary, tertiary, and quaternary radiation emitted from the shielding itself can be more dangerous than the initial particle that simply zips right on through lower-density materials without causing any problems.

I forget who wrote it, but one comment early in the space race said something to the effect that Man was safest in space with just enough shielding to keep out the UV and keep in the air.