Basically, if this works as the headline suggests, and my poor understanding of the paper implies we can take their example of competing financial institutions:
Two banks share data, that is intended to be secret, and they use this technique to compute some property over the data. Each bank can then do the same computation over there data alone, and compare the resulting model over their data and the result over their competitor’s. From that they can infer the properties of their competitors portfolio, which seems to be leakage of data that is not intended to be possible.
Hence I am clearly missing something, which isn’t unexpected as HE is unintuitive to me.