The US Code of Federal Regulations says (36 CFR 261.10)
The following are prohibited:
(a) Constructing, placing, or maintaining any kind of road, trail,
structure, fence, enclosure, communication equipment, significant
surface disturbance, or other improvement on National Forest System
lands or facilities without a special-use authorization, contract, or
approved operating plan when such authorization is required.
(b) Construction, reconstructing, improving, maintaining, occupying or
using a residence on National Forest System lands unless authorized by
a special-use authorization or approved operating plan when such
authorization is required.
Though it's harder to find the applicable code section, multiple Forest Service notices about illegal structures (e.g. this notice about illegal conical stick structures) say the following:
Violators are punishable by a fine of not more than $5,000 for
individuals and $10,000 for organizations, imprisonment for not more
than six months, or both.
A fire ring and a few logs do not constitute a structure or a significant surface disturbance. In some areas (heavily used, ecologically sensitive, or high fire danger) the Forest Service will prohibit constructing new fire rings, but elsewhere, these are not LNT but they aren't illegal either.
Camp benches border on being structures. An isolated camp bench may not be illegal; start setting up a bunch of them, and the resulting amphitheater will certainly run afoul of 10(a). A long-term wooden shelter is definitely not OK, violating both (a) and (b). Simple survival shelters (e.g. lean-to) are supposed to be dismantled and the materials dispersed when you leave the site.
I know this has been many years since the question was first asked, but the answer that has been marked as correct is dangerously bad advice, both legally and ethically. Saying legality doesn't matter and suggesting that you skirt possible problems by hiding from others is the kind of "how much can I possibly get away with" attitude that is responsible for widespread and lasting damage to our public lands. On your own land, do what you please. On public land, leave no trace.