The results are not really as small scale as you portray. The article cites other similar studies:
"Four previously published studies support our conclusions. First, a prospective, observational study among Native Americans from 2002 through 2005 found that infants of vaccinated mothers had a 41% reduction of the risk of laboratory-confirmed influenza infection in the inpatient and outpatient settings as determined by viral culture or antibody titers (relative risk, 0.59; 95% CI, 0.37–0.93).20 A second study, a randomized controlled trial of maternal influenza vaccination during pregnancy, was conducted in Bangladesh in 2004 through 2005. In this tropical country with year-round influenza circulation, investigators reported fewer rapid test–confirmed influenza cases among infants of mothers who received influenza vaccine compared with infants of unvaccinated mothers (6 vs 16 infants, respectively) for a vaccine effectiveness estimate of 63% (95% CI, 5–85%). Among 110 infants in the influenza vaccine group and 153 infants in the control group, vaccine effectiveness against unspecified respiratory illness with fever was 29% (95% CI, 7–46%).19 Third, a matched case-control study compared hospitalized infants with physician-ordered direct fluorescent antibody for seasonal influenza from 2000 through 2009. Cases with a positive influenza test result and controls with a negative test result were matched by date of birth and date of hospitalization. Maternal vaccinations were included only if they were confirmed and given at least 14 days prior to delivery. Effectiveness of maternal vaccination among infants <6 months of age was reported to be 91.5% (95% CI, 62–98%).30 Fourth, a Northern California Kaiser Permanente database study over 5 influenza seasons (1997 through 2002), found that maternal vaccination was associated with a decreased risk of pneumonia or influenza hospitalization in their infants with an adjusted hazard ratio of 0.63 (95% CI, 0.30–1.29), translating into 37% protection.31 Our 95% CIs for protection of maternal vaccination from influenza hospitalizations among infants <6 months of age overlap those from each of these studies."
You stated "Quite clearly, the mothers who were vaccinated also tended to be more affluent and the non-vaccinated included a higher percentage of minorities." Note that the other studies included subjects in Native American and third world populations.