As a coach, I will say that form, most certainly, can be taught. In fact, it's what we do a lot of the time. Some kids naturally have better form than others, although everyone learns form and continues to perfect it.
I would however say, that sometimes natural limitations interfere with form. For example, I have a wonderful gymnast training level 5 who works super hard, listens well, and makes corrections. However, no matter what she does, her arms never straighten all the way. Her older sister was the same way. Perhaps it's genetic, but even when she straightens her arms as much as possible, they still look quite bent. There is no point in pushing her to straighten her arms, as it isn't humanly possible for her. We just focus on all the other fine points of form.