No. The model has a problem with overfitting. That’s my point.
Saying it doesn't make it true.
You are claiming there is a generalization problem that causes extra error in practice. Another perfectly viable hypothesis is that the classifier is working fine, it's just tuned for true positive rate and accepts a higher false negative rate to get it. Specificity vs. sensitivity is a fundamental trade off, not a training issue (though that can make both worse)
So this sucks if you don't fit the model well in a way that has you often end up as a false negative - but that doesn't' mean the model is broken.