Unequal group sizes and chi square test of independence

#1
I began working on a project that compares birth outcomes of women in a case management program (n = 270) to the birth outcomes of the general population of delivered mothers in the state (n = 56,001). We were critiqued for testing with chi square for group differences on several birth outcomes in the vital statistics data that are recomputed into dichotomous variables (e.g., pre-term (Y/N), low birth weight (Y/N)). The critic stated that the group size of 260 was too low to run the chi square test. Because the smallest cell size in the crosstabulation had an expected value of 70, I don’t think this is a valid concern. All I can think is that perhaps the person was expressing concern that the group sizes are so drastically unequal in size.

I have hunted peer-reviewed journals, statistics forums, and google for guidance on whether using chi square is problematic when group sizes are unequal. I know this is a problem with parametric statistics because of the underlying assumptions but I can find no evidence that it is a problem for non-parametric statistics like chi square test of independence, however, I can find no statement that says it is NOT a problem. I do understand that chi square is sensitive to large sample sizes, but how does this play out when one group is very large and one group is about 250?
If there is a problem with using chi square to detect group differences (dichotomous variable) in birth outcomes (dichotomous variable), what are alternatives to examining group differences? I appreciate your help in advance.