FWIW I read an article about this yesterday. The students recognize that thier balloon could not / did not reach "space" much less "outer space". They refer to their photos as from "near space". It is the typical yellow journalism that is embelishing.
I recall that they determined the balloon reached an altitude of apprimately 93,000 ft (17.6 miles).
They intend on offering all the details of what they did online for a fee of about $150, so actual cost to others that may want to repeat their experiment would be ~$300. ($!50 for the directions and $150 for the materials).
Pretty neat stuff.