Im not so sure about it. Hmm... We have tested our concept with a bunch of physics and an astronomer, and we think that (of course not in our galaxy) this is possible. You're right - the rotation of Bachus is strictly synced with it's orbit (everything was based and tested at the model of Earth and the Moon). In fact, from physical point of view - Bachus didn't exactly stopped to rotate - but it's rotating nearly exactly the same around the planet as the Moon around the Earth - the time, that is needed to rotate over 90 degress is nearly the same as time needed by Bachus to travel 1/4 of it's orbit (it goes around on the circular, not hyperbolic orbit). In this way, changes of the border of light are relatively small (about 200 miles per year periodically), but this don't changes so drastically the fact of dividing the planet on two parts.
The only thing, that pretends me to call this planet stopped, is the technologic level of people that are living on is not such big enough, to prove this matter of facts, so they think (and also this information is passed in the public fame) that they planet has stopped.
And stay calm - they not gonna burn themselves. Temperature didn't go up - Bachus is still at this same position, so any changes of temperature or climate didn't went on it's surface - those are things linked with the move across the orbit, not around oown axis. Of course - at the first years people, don't used to the new way of living, was dying (about 25% of population on the light side), but crisis is forcing the evolution. Currently, on the light side there are living people, which were strong enough, to live in that conditions. At the planet surface there are still climatic zones - tropical, temperate - even polar, because the sun don't affects it's so much (they are living in the permanent 'greenhouse effect climate', but, after 500 years, they already learned how to survive.
But, of course, we didn't have any experiment, which would without any doubts state that this is possible.