Natural birthing and timing

So, recently my contractions have been increasing and it's beginning to start being where I can time them. Obviously they're still far apart as I'm only 35 weeks. However, today I went to the OB and they told me that if I were to start labor before 38 weeks that they would try and stop the labor before it got too far. MY question is, if my body is that close and telling me that it's time, then shouldn't it be okay? I really want it to be all natural. AND I have read a good bit of stories of women who went into "early labor" and the hospital stopped it, they then later had to have c-sections because the baby was too big or they couldn't seem to push them through.