Came across this today. A co-worker had a shared LOV based upon a query that used a REST Enabled SQL data source. The LOV worked fine except when used as a checkbox group. A little sleuthing pointed to a solution, though it's really an APEX bug, I think. In short, the alias of the display column must be DISP and the value column must be VAL. So change
select col1, col2 from my_table
select col1 disp, col2 val from my_table
That solves the issue. I suppose I should also log a bug.