The first misnomer here is that Batiks are more tightly woven. Not exactly. Some batiks (not all) will have a higher thread count in order to take the dyes better and hold up to the wax resist method of dying. Usually a threadcount of around 200. Additionally the wax resist method calls for the fabric to be put in boiling water to melt the wax away. This causes the fabric to shrink up a bit and appear to be more tightly woven. Some batiks are much harder to hand needle than others. And I have heard of and read here, issues of when the batik is longarmed that the needle holes are obvious. Usually a washing will once again "re-arrange" the threads in the fabric to close up the hole. Rarely have I read or heard of a longarm needle actually breaking the warp and weft threads in batiks.
High thread count sheets (300 or more) to my knowledge are only semi-shunned when longarming when the larger size needles are used. Because there is so much fiber packed together the longarm needle can actually break the warp or weft threads making a hole and weakening the fabric (as opposed to sliding between the warp and weft threads). this is due to the much larger size longarm needle. I suspect a domestic sewing machine needle is fine enough to still slide between the warp and weft until you start getting into those really high thread counts (600+)
The 2nd misnomer is it is a big deal. I really don't think it is. What I suspect happened is at one point in time a bunch of quilters gave longarmers sheets for backing and the results were less than spectacular and they weren't warned up front. So a few complaining loudly about it, turned to many and more and more longarmers found out so refused to take sheets or warned that the end product could be less than satisfactory. Maybe someone got cited for it at a show. As most quilting folklore happens, word spreads and the beginning circumstances are forgotten and it gets blown into a full fledged infraction by the quilt police.
Of course it can be done and many longarmers don't have issue with it. and many clients don't care if there are irregularities in the finished product as long as they are warned up front. It does make a very annoying "thwok thwok, thowk" noise. It can play havoc with tension and it can also create snags in the fabric (kind of like a run in nylon only it is only one or two thread widths wide and usually only spans a short distance of a few inches).
I have never had issue with Batiks or batik wide backs. I have had issues happen with high thread count sheets, no issues with flannel sheets.