I think the term "unassisted birth" is generally used not to literally mean that the laboring woman has no assistance, i.e. no help or support of any kind, but that there is no professional birth attendant present. The definition is not obvious, so to me it's not a very useful term, but it's become convention to use it.
Personally, the words that are more useful to me are "unhindered", "spontaneous", "instinctive", etc. Ask yourself not whether your birth was unassisted, but was it made to be dysfunctional? If so, then the question becomes: what do you need to do so that it won't be next time? Probably that answer will be different for each person.