You can end up with a Ph.D. in some fields being exposed to almost no statistics, or only statistics which work in very confined settings (certain experimental sciences where "Just do an ANOVA... is genuinely the answer to almost every question).

That often works...right up until the moment when a scientist has to step outside that context.

This often cuts both ways though. I have seen beautiful math and statistics around problems that don't make any sense if you've taken more than one semester of microbiology.