Only have one small thing to add to Jesse's answer.
Even in Standard Japanese phonology, /h/ is pronounced differently in ひ than in, say, は, which makes it sound a lot closer to /sj/. How close the pronunciation is for individual speakers, as Jesse says, is dialectal, and even depends on the specific word.
Another factor may be that many speakers don't or hardly pronounce the /i/ sound in ひと. I feel that this makes it harder to hear the difference. For example, ひいて and しいて (where the vowels have to be pronounced) seem easier to distinguish than しく and ひく (where the vowel might not be pronounced as clearly).
Incidentally, one of the most common examples of the (opposite) phenomenon is 敷{し}く which many pronounce as ひく. Not sure if it goes the other way as well.