using the nominal scale in the rules, a legion is something between 16-20 elements for Middle Republican, Later Republican, and Principate Romans. So a whole legion clearly exceeds the possible 4,6, or 8 elements in the lists
For Dominate Romans, the Legions were smaller, and 4 is the right number (plus 2 elements of bows if desired). Anything larger would be ahistorical
The correct organizational term for units in the Late Republican and Principate Romans is cohort, and the number of baes in these units is TWO, with the exception of 'double-strength' cohortes (cohortes millaria) which would be 4. Which means for these armies, the FOG battle group does not correspond to any formal organization, representing instead multiple units working together. So using the smallest possible BG is not 'cheesey' as it still represents either two cohorts of standard size or a single a millaria cohort, of which one-and only one- existed in a legion, and Roman armies tended to have (with some exceptions) at most one or two auxiliary cohorts reaching 4 elements in strength.
For Middle Republican, the cohort was a flexible organization, but started at 6 centuries and would include triarri - an impermissible battle group in FOG. The other alternative is an entire acies of hastati or principes, and FOG's list makes this impossible by declaring the units to be mixed. The discussion of 'legions' in the FOG list is not consistent with the scale, and I take it as saying you must have either BGs of 4's or 8's not an attempt to describe any real organization.