You can have a screaming high djembe with 6 mm rings, no problem. It's mainly about applying tension evenly (by having enough loops) than the strength of the steel. Both 6 mm and 8 mm steel bend quite easily; the reason steel is called "strong" is its tensile strength, not its stiffness.
Depending on the skin, it can happen that a skin stretches more across the spine than along the spine, so you end up with a dip in the rings at 90 degrees to the spine once you apply tension. But they tend to spring right back; if not, just use them rotated by 90 degrees next time.
If I have grossly bent rings, I just bend them back as best as I can. Once the skin is mounted, the tension on the verticals quickly straitens out the rings anyway. So, all good, IMO. Just bend them back, and go ahead. The drum will still turn out fine