99% of sugar sold in the US is grown and processed here. There is a huge tariff placed...
...on sugar grown anywhere else in the world, so as to protect US sugar growers.
Beets are much easier (hence cheaper) to grow in our climate, since sugar cane requires semi-tropical temps. (Hawaii is the best place to grow sugar cane in the US. "C & H. Pure cane sugar. From Hawaii. (from Hawaii) Growin' in the sun. (growin' in the sun)", etc......).
So, as you say, unless is says "Pure Cane Sugar", you can rightfully assume it is beet sugar.
Michael