Dizygotic twins can appear, in rare instances, to share a sac. They don't come by it in the same way that monozygotic twins do. There are two 'sacs', BTW...one that holds the amniotic fluid (the amnion), and then one that surrounds that (the chorion--I think I'm right on those names, but it's been awhile). In the case of DZ twins, there could be a perforation of membranes that then heal and grow together. However, you'd think that there would also be problems of arm and/or leg malforations because of the bands of ruined membrane...but as long as there was enough fluid that might not be a problem.
Once the placenta is out, it is VERY HARD to determine where the membranes were unless it's sent to pathology for the equivalent of an autopsy. Those folks wouldn't have a problem...but a glance by the OB in the delivery room might lead to misleading surface judgements.
Scientists know VERY little about twinning, what causes it, and what all can happen (especially stuff that goes wrong). Twin To Twin Transfusion Sydrome (something that arises when twins share artery-to-vein vascular connections through the placenta) is almost exclusively something that happens to MZ twins, but there have been one or two cases of it happening in DZ twins (both involved zygote transfers though, so they think that perhaps it was related to something mechanical). It's also possible for MZ twins to be in a situation where one has a chromosomal disorder and one does not. Unfortunately, most twin placentas, even MZs-with-problems, are NOT sent to pathology and if they are the results are not collected in a database (which would be invaluable to studying these things).
Our boys had severe TTTS at 16 weeks, and we qualified for a somewhat rare and still experimental surgery one week, but then things alternated improving and getting worse, which nocked us out of the surgery possibilities. By the time of birth, our 'donor' and 'recipient' twins had *switched off*, which has never been documented before. (And they both survived, despite early onset with no intervention. And Dylan went from absence of distolic blood flow--essentially his blood would move backwards inbetween heartbeats...NOT GOOD--to completely normal within 4 months. ) Our pathology report is being sent to several databases. Many of the specialists we talked to during the course of my pregnancy admitted that scientists/doctors know practically zip about placentas, how they're formed, how they get hurt, why they function they way that they do (either poorly or not), ect. And placental problems are fairly common. So I'd venture to say that science is largely ignorant about the whys of conjoined twins or if they necessarily MUST happen solely in MZ twins (though again, if it were to happen in DZ twins the mechanics would be different, of course.).
I think the answer to your question is that NOBODY really knows. It certainly might be possible, or evidence might look like it--but no one will know if that that's really what's happening.
I used to find this sort of stuff fascinating, until it was necessary for me to learn about it. Now I know too much (little?) for my tastes. I really wish more brilliant minds were researching THIS type of thing than nuclear weapons though.
Edited again to add: Oh yeah, to add to the confusion and possibilities, scientists also now believe that sometimes one egg can divide pre-fertilization. So you could have a pair of twins that's technically from one egg, but still developed from two zygotes. Which is why terms like 'MZ' and 'DZ' twins are more accurate than identical and fraternal--but in this particular case I think that really blurs the line.