Not in the way that people usually use those words. "Reasonable position" generally refers to a reasonable assumption to make or gamble to take. Something technically remaining within the realm of possibility is not that.
And your personal opinion on this alleged standard is relevant because…?
Edit: clarified the question
Because the two of us appear to be attempting to communicate and effective use of language requires some level of mutual understanding of vocabulary. The statement you made does not hold when those words are taken to mean what I broadly understand them to mean.
Which is to say that no, a very slim chance is not a reasonable position to take in most contexts.