This story keeps getting more confusing. It sorely needs to be edited by a math-literate person.
Here's the background of the story:
Here's the diagram in question:
The Golden Ratio (with a capital Phi) is the long side divided by the short side. This is 1.6180339887…
The short side divided by the long side is 1/Phi which is [sqrt(5) -1]/2, which is lowercase 휙 [http://mathworld.wolfram.com/GoldenRatio.html].
The kid got it wrong for not reading the ratio correctly (short divided by long), but the museum will get it wrong if it just replaces minuses with pluses (and uses capital Phi for the conjugate ratio).
Here's a great article on Golden Ratio misconceptions:
http://www.cdlmadrid.org/cdl/htdocs/universidaddeotono/unioto/matematicas/markowsky.pdf