It's not inherently true. Technically, deep learning is essentially any neural network model with hidden layers (i.e., one layer in between the input layer and the output layer). You could have a "deep learning" model with a couple dozen parameters, perhaps. But at that end of the scale, most people would probably reach for other approaches that are more easily interpretable (e.g., logistic regression, random forest). So in practice, yes, virtually any deep learning model you see out there in the wild, even most "toy examples" used to teach machine learning, are going to be overparameterized.

depends on the model, but most systemns I've worked with had millions to billions of parameters, and trillions of (sparsely populated) data points.

Not even close, most of my work has been in naturally occurring data and there is way waay more data available than can possibly be used (petabytes). Where they get this idea as being the rule and not the exception is beyond me.

DL cannot be over-specified. However you do need to mind your endogenous and exogenous variables.