If you look on the second post down, you will find there are a number of ways of measureing the speed of light apart from atomic processes.
The fine structure constant change, or apparent change (which is well within the range of observational/instrumental error, by the way) does not reflect on c, as hc is always constant.
It was suggested by Andreas that the measured changes in light speed were not correct for three possible reasons:
Alternatives, which aren't in contradiction with modern physics:
1) The values aren't correct
2) Other measurements with the opposite trend were simply left out
3) Simply chance
1. The values were consistent and showed a consistent downward trend despite any error bars
2. No data was left out
3. Baloney. The probability that hundreds of measurements over several hundred years by dozens of highly intelligent and qualified men would ALL be chance is so vanishingly small that you might as well figure the sun will explode today!
A number of constants, in the meantime, have changed. Here is a chart with the references of just two besides the speed of light:
http://www.setterfield.org/Charts.htm#graphs
I would suggest, Andreas, that you have been swallowing whole, without checking for yourself, something you have been taught in school. We all did that at first. But if you check the data itself, you will find you were not taught truthfully.