Yes. Whenever your on a slab, you can request permission to either build for yourself or for your faction. If I'm understanding that correctly, they requested permission to build, but you haven't accepted their permission, meaning they cannot build. Until the owner of the slab accepts the build request, no construction can start.
Only reason otherwise would be if the slab owner and builder are one and the same, or the builder is in the same faction as the faction that owns the slab and has the build privs.