As a statistician-and-engineer who is currently on the job market (my graduate program finishes this spring), I feel this pain.
I've been referred to as a "data scientist" multiple times (that's even been my official title at work before), though I do still cringe sometimes when I hear the word, for this exact reason.
That said, I don't usually present myself as a statistician, even though my degree is a statistics degree. Most people who hold statistics degrees are fairly lousy engineers[0], and I don't know of any other term that (concisely) expresses that I'm equally competent as a statistician and a (backend) engineer[1].
Of course, this is because many of these programs haven't yet caught up to the fact that computers exist and are still teaching statistics as if we're in a pre-computation era. The perfect solution is to fix this, and thereby fix the connotation of the word "statistician".
It's the same reason I dislike the term "growth hacker" - really, that's just the way marketing should be done (ie, based on numbers and verifiable statistics). In a perfect world, all (competent) marketers would be "growth hackers". But many marketers aren't, and so we have to make up another cringe-worthy term for it.
Unfortunately, that's a problem that's beyond my means to solve. So I bite my tongue and add the word "data scientist" to my resume anyway.
[0] Usually self-proclaimed, too [1] ie, "I could work as a backend engineer if I wanted to/needed to, but I'm looking for work involving both skillsets"