This typically occurs when a package has an upper bound on the supported Julia version, either in REQUIRE or directly in METADATA. In this case the bound was introduced in https://github.com/JuliaLang/METADATA.jl/pull/17104.
Usually this is done as part of the upgrade to 0.7/1.0, to make sure that incompatible versions can’t be loaded in 0.7 or 1.0, and followed up by new compatible versions with higher bounds. Sometimes when there’s a gap between these, it works to pkg> add Package#master in the interim.
NamedTuples is a little special though since named tuples are now part of Julia Base and users of NamedTuples should migrate to using the Base functionality instead. Thus upgrading the package for Julia 0.7 is understandably not a high priority, but I’m sure a PR which does the upgrade would be well received anyway.