I have had the exact opposite experience with machine learning and statistics. In my experience, those who come from the 'statistics' side tend to use constructs, like null hypothesis significance testing, which are not consistent even from a theoretical point of view. And further, when they use them, they do awful things like p hacking, or using a direct comparison of t-stats as a model selection criterion, which are further rife with theoretical problems, not to mention lots of statistical biases and so forth.

I find the machine learning approach is far more humble. It starts out by saying that I, as a domain expert or a statistician, probably don't know any better than a lay person what is going to work for prediction or how to best attribute efficacy for explanation. Instead of coming at the problem from a position of hubris, that me and my stats background know what to do, I will instead try to arrive at an algorithmic solution that has provable inference properties, and then allow it to work and commit to it.

Either side can lead to failings if you just try to throw an off-the-shelf method at a problem without thinking, but there's a difference between criticizing the naivety with which a given practitioner uses the method versus criticizing the method itself.

When we look at the methods themselves I see much more care, humility, and carefulness to avoid statistical fallacies in the machine learning world. I see a lot of sloppy hacks and from-first-principles-invalid (like NHST) approaches in the 'statistics' side. And even when we consider how practioners use them, both sides are pretty much equally as guilty of trying to just throw methods at a problem like a black box. Machine learning is no more of a black box than a garbage-can regression from which t-stats will be used for model selection. However, all of the notorious misuses of p-values and conflation over policy questions (questions for which a conditional posterior is necessarily required, but for which likelihood functions are substituted as a proxy for the posterior) seem very uniquely problematic for only the 'statistics' side.

Three papers that I recommend for this sort of discussion are:

[1] "Bayesian estimation supersedes the t-test" by Kruschke, http://www.indiana.edu/~kruschke/BEST/BEST.pdf

[2] "Statistical Modeling: The Two Cultures" by Breiman, https://projecteuclid.org/euclid.ss/1009213726

[3] "Let's put the garbage-can regressions and garbage-can probits where they belong" by Achen, http://www.columbia.edu/~gjw10/achen04.pdf