Since the specification is written and a part of the construction documents, you are never wrong if you enforce then to the "T" and can document the conditions are to properties, temperatures and time. Shutting down a project can be a very big and attract a lot of attention from your firm's pricipals, the contractor and the owner, so have to make sure you are right.
One of the big factors in cool weather construction. If the construction is done quickly and well organized, it can be with no problems. Even a 1600 sf lowly full height block basement can be started and built at -10F or 0F, if it is quick, planned and protection is provided. Usually it is a 4 day job from start of excavation to completion, but with no backfilling since it is preferred by the G.C. and owner to backfill and pour the slab later after other work is done. The key item is the timing, scheduling and protection of areas.
If your voids to be backfilled have been setting unprotected for a while, the frost "depth" is immaterial because freezing knows no direction and can freeze horizontally also. Even at 21 to 32 for daytime AIR TEMPERATURES, the exposed surfaces can freeze if exposed for extended period because evening temperatures are usually lower, plus there is more radiant heat loss.
Your situation is a matter of judgment (keeping in mind the accepted specifications) plus what the construction schedule will dictate for timing. If you have documented information on the conditions, any prior approval from your principals you can get for being a "hardnose" will help greatly if there objections or job delays.
Dick
Engineer and international traveler interested in construction techniques, problems and proper design.