There is a vast difference between strong advocacy to have a child's needs met, and pushy parents of the tiger-parenting variety. The child's love of learning was mentioned by another poster upthread, and can be utilized as an easy distinction between the child's comfortable pace/depth of learning and a child who is hothoused, pushed, tiger-parented to become a trophy child. In general, pushy parents may seek to have their students accelerated in both ELA and math, while remaining at grade level with the specific motivation to have the child's test scores be superior to those of their classmates who've had less exposure. This is different than an child whose needs in ELA and math require advanced academics in those areas but who is otherwise not a candidate for whole-grade acceleration(s).
While a school may have had students who were "hurt by acceleration", this may be due to improper fit or improper implementation. Some may say that in these cases the home/school team would be wise to conduct a post-mortem review to see what might have been done differently. For example, in some cases beginning with the IAS to assess proper placement may be a factor, a school attitude of support for accelerated students may be another.
In the final analysis, teachers know the child for a short while, parents are in the relationship for life; Parental input ought to be heavily weighted in decisions. Documenting decisions, as the IAS suggests, may help both teachers and parents carefully weigh the pros and cons in each situation.