>Pardon my ignorance, but isn't that the theory of cosmic inflation, not precisely the big bang theory?

There are a few things at play here.

1. There is the observation that the further away a galaxy is from us, the greater redshift of the light coming from it
2. The interpretation of this data is that the galaxies are moving away from ours; unless our galaxy is somehow unique this can only mean that the universe is expanding
3. The theory of the Big Bang is proposed as the beginning of an expanding universe.

The paper I cited argues that the interpretation in 2 is incorrect as can be shown by the lack of time dialation in supernovae light curves. If 2 is out, then 3 must be out as well.