You have stated something that someone with a high school-level (e.g. superficial) understanding of probability/statistics would understand. Most research in neural networks requires only a very superficial level of statistics.

There are certainly many areas of neural networks where statistics is important (more theoretical areas), but those don't form the core of the research field.

Also, calling (stochastic) gradient descent a form of statistical inference, while technically correct, is a ridiculous stretching of the term. No researcher considers SGD to be a statistical inference algorithm.