I have been running for a few years now, and this question still bugs me. I asked around with my friends, and got a mix of replies, yes, no, depends, maybe..., you get it.
So, I thought why not ask the community here, a place where I visit often. What's your take on this. If I run 13.1 miles in training, can I say that I have run a half marathon?
Why do you care what anybody thinks? Why do you need to label your run? Why are you so insecure?
I was doing a long run once out of town training for a marathon, was trying to do a 22-24 mile run (only really wanted to do 22 but was estimating the distance on trails), I ended up missing a trail and by the time I was back to my car I had run 32 miles. Really really crappy day. I don't tell people I ran an ultramarathon, I do say I once did a 32 mile training run.
(Side note, I did get a PB in the marathon I ran 4 weeks later. I do not however advocate a 32 mile training run, or the discomfort of being lost a long way from home.)