Very young children (under 2 years old) have high risk for influenza-related complications. Children 6 months or older in the US are recommended to receive influenza vaccination annually, yet uptake is substantially lower than other routinely-recommended vaccines. Existing nationally-representative studies on very young child influenza vaccine uptake has several limitations: few examine provider-verified influenza vaccination (relying on parental report), few contain parental vaccine attitudes variables (known to be crucial to vaccine uptake), and none to our knowledge consider intersectionality of social disadvantage nor how influenza vaccine determinants differ from those of other recommended vaccines. This nationally-representative study examines provider-verified data on 7,246 children aged 6-23 months from the most recent (2011) National Immunization Survey to include the restricted Parental Concerns module, focusing on children up-to-date on a series of vaccines (the 4:3:1:3:3:1:4 series) but not influenza vaccines ("hidden vulnerability to influenza"). About 71% of children were up-to-date on the series yet only 33% on influenza vaccine recommendations by their second birthday; 44% had hidden vulnerability to influenza. Independent of parental history of vaccine refusal and a myriad of health services use factors, no parental history of delaying vaccination was associated with 7.5% (2.6-12.5) higher probability of hidden vulnerability to influenza despite being associated with 15.5% (10.8-20.2) lower probability of being up-to-date on neither the series nor influenza vaccines. Thus, parental compliance with broad child vaccine recommendations and lack of vaccine hesitancy may not indicate choice to vaccinate children against influenza. Examination of intersectionality suggests that maternal college education may not confer improved vaccination among non-Hispanic Black and Hispanic children despite that it does for non-Hispanic White children. Policymakers and researchers from public health, sociology, and other sectors need to collaborate to further examine how vaccine hesitancy and intersectional social disadvantage interact to affect influenza vaccine uptake in young US children.