From the article you posted:
"...By eliminating the dimensions of units from the parameters we can derive a few dimensionless quantities, such as the fine structure constant and the electron to proton mass ratio. These values are independent of the definition of the units, so it makes much more sense to ask whether these values change. If they did change, it would not just be the speed of light which was affected...."
There are a lot of vsl theories (thats varying speed of light, fyi).
You have this:
http://arxiv.org/abs/0708.2927
The VSL Discussion: What Does Variable Speed of Light Mean and Should we be Allowed to Think About ?
and this one:
http://arxiv.org/abs/hep-th/0505034
Quantum Creation of a Universe in Albrecht-Magueijo-Barrow model
and this one:
http://arxiv.org/abs/hep-th/0502070
Quantum cosmologies with varying speed of light and the Lambda problem
http://arxiv.org/abs/gr-qc/0404066
Variable Speed of Light Cosmology and Bimetric Gravity: An Alternative to Standard Inflation
http://arxiv.org/abs/astro-ph/0305457
New varying speed of light theories
I'd be happy to muddle through these highly technical papers with you if you're honestly into questioning the implications of einstein's relativity.
