It depends on how you define "produced" and "nuclear energy". Without more details we can only speculate, but the possibilities are very limited.
The link you cite appears to be by someone who has constructed a Farnsworth Fusor (or possibly some variant on the same theme). These devices make interesting (if expensive and advanced) high school science projects, but the amount of energy they produce from fusion is always much less than the amount taken to drive them. It is most likely that this girl has done something similar. If so then the claim is theoretically sort-of true, but from a practical point of view it's really false as "produced nuclear energy" usually means getting more energy out than you put in.
Nobody has yet managed to produce net energy by fusion (except for H-bombs). There are serious attempts to do so, but they are some of the biggest of big science projects. I think we can discount the possibility that this has been accomplished by a hobbyist. If it had, it would literally change the world: no more global warming, every oil state goes bankrupt, probably every power company goes bankrupt too. And that's just for starters.
It is also very unlikely that this student has produced energy by fission. To do so would require enriched uranium or plutonium in significant amounts, and doing so at home would be hazardous in the extreme, not just to the people in the house but to anyone in the same city. The case of the radioactive Boy Scout is instructive. Note that Hahn never achieved criticality; merely trying to generate the fuel created serious contamination and exposed him to dangerous levels of radiation.