Not a personal experience, but I have a funny story about this.
A few years ago I worked in the polyclinics in Bridgetown, Barbados. (Polyclinics there are considered one-stop medical shopping; they're designed to make medical care less threatening and more accessible for their mostly poor and undereducated population. Completely fascinating experience.) I worked in their antenatal clinic and had a wonderful time.
Keep in mind this is a world of true midwives - u/s and scans that we First World women take for granted are almost unheard of unless you're perceived as having a problem - and of Third World economics - the most interesting thing I saw was how a long line of pregnant women would bring in their FMUs in carefully cared for specimen cups (you know, the ones we toss at our MD's offices and in hospitals without thinking - the sisters - what they call RNs - and midwives there taught every patient how to wash it carefully in very hot water and how to let it air dry, and these women, many of whom lived in shacks with dirt floors, did it to the letter). The major national hospital was right across the street, and when I was there I saw a preemie who had an O2 tent made out of one of those Glad disposable plastic container (and it worked, by God - proof that modern medicine isn't always the perfect answer - their hospital acquired infection death rate is actually LOWER than ours - as I said, fascinating - a world where MRSA is a rarity - no matter how much faith I put in First World medicine, we could learn a LOT from the Third World as well.)
Anyway, the chief midwife and I were doing manual exams (this is how they guesstimate fetal age) and while I was performing the manipulations we actually physically WATCHED THE BABY SHIFT POSITIONS - I FELT its little head turn beneath my hand and her belly went from sticking out to almost flat as it happened! You'd pretty much never experience that here in the States in a conventional MDs office! The mom and I just looked at each other with that "WOW" look and she said, "He's (she was convinced it was a boy) never ever done that before!" Coolest moment I've ever had as a nurse.
So yes, your belly can shift - and what you might be feeling as hard could actually be his/her head, because when they shift they push all that aminiotic fluid around and move it up and down and exert different pressures as they do it. I've also been told if it's your first kid, things can happen that you don't recognize as actual fetal movement because you have no idea what's going on in there because you've never experienced it (I'm making assumptions in your case but hope they're helpful!). Like the stories you hear of first time moms at around 16, 18 weeks who complain of intermittent stomach cramps and gas? A lot of times that turns out to be kicking, but they don't know it because they've never experienced it!
