Hi–That advice certainly has its merits. To help you with your list, you might also be interested in the top Ph.D.-feeder schools in STEM – Here are some tables from the National Science Foundation – if you scroll down – the list is a little old but it may give you a ballpark idea of some schools and their STEM strength.
https://wayback.archive-it.org/5902/20160210152803/http://www.nsf.gov/statistics/infbrief/nsf08311/