My 2c: running can naturally be part of a hike - probably not a major part (as my idea of a hike is a backpack & hiking shoes), but surely on the parts that you want to get through quickly for whatever reason - weather, need to be somewhere on time, etc. While being considerate of others on the trail of course.
But marking a hike as a “run” just because if that? Tbh that doesn't make much sense to me. If we use the same logic, just from the other side, we could say “there was some walking included so it can't be called a run.”
There are trail runners and there are hikers, and both often combine walking and running. And if you want to distinguish what's what, simply go by the purpose of the activity.
@Jana_S - Here is another way to look at it. Since there are segments that are specific to run and segments specific to hike, it would seem that you would want to be on the conservative side. If you walk or “hike” some during a run, you are not doing something that might take someone’s KOM/QOM, you are just going a little slower on average. No harm, not foul. But, if you are running some while calling it a hike, you are, in a way, cheating, by using an activity that is faster than what the claimed activity is and possibly taking someone’s “hike” KOM/QOM because you are running portions of it. If you are mixing hiking and running, I would call it all a run.
@anchskier I totally understand what you mean, though as long as there's no vehicle/wheels involved, there's no exactly defined line between the two activities… let's say I do a 20k hike and run a 200m part of it to hide from rain - and it happens to be a “segment”: do I have to mark the whole 20k thing a “run”? That doesn't make sense 
If I get my running shoes and go for a run, I save the activity as a run, even if I walk some portions of it. If I take my hiking shoes and a backpack and I go for a hike, I save it as a hike, even if I decided to run from a hill to catch my bus home.
@Jana_S I do see how tiny runs (e.g., catching a bus or crossing a street when Don’t Walk is already flashing) as part of a long hike or walk probably don’t make the whole thing a run. But segments are usually longer than that, and if you run most or all of such a segment, it does distort the segment statistics.
I’ll also disagree with your statement that “there's no exactly defined line between the two activities.” The racewalking events at the Olympics are carefully judged to make sure that competitors who run are disqualified. From the racewalking Wikipedia page: “...it is different from running in that one foot must appear to be in contact with the ground at all times.”
I lean towards @anchskier ‘s response, but that was my bias from the beginning. It is useful to know that the opinion of some in the community match more closely with the person who “took” my hiking segment, so my black and white thinking should perhaps allow for more gray.
