Again, an increase in cosmic ray levels striking the Earth is only one possible cause for the observations.
Oddly enough, while no expert in the field, I did spend a decade working with high resolution radiometric and magnetic survey equipment measuring the global magnetic field, local and diurnal variations, ground radiation and performing numerous high altitude stacks to plot the falloff of cosmic ray intensities through the atmosphere. This was performed in both hemispheres and near both poles and totalled several million line kilometres. Writing the software to process all that data gave me a little insight into the issues and the opportunity to work with people that had spent their careers in the field.
What the spikes tell us is that there was minor increase in isotope production, most probably in the upper atmosphere.
Clearly this could be driven by either an increase in raw material in the upper atmosphere (equatorial volcanic explosion is one possibility), or an increase in cosmic ray levels within the atmosphere (variations in the global magnetic field lines could account for that) OR an increase in the amount of external cosmic rays (which brings us to the guesswork being expounded in the article you so kindly quoted).
I'm no expert either, but I was under the impression that the paleomagnetic record is pretty good for at least the last thousand years. So a magnetic variation which could cause a 20-times-normal variation in the production of carbon-14 (from 5/100 of a percent to 1 percent) would have left some evidence?
Likewise for volcanic explosions, especially considering the narrow time scale; enough material was pumped into the atmosphere to cause that 20-fold increase in variation, but its effects were gone in a year or less?
Anyway, I know that mainstream science reporting is not the best, but just because scientists don't explicitly say "we've considered alternate explanations and found them less likely" doesn't mean they haven't done that.
From the wikipedia account, assuming it's accurate;
> The 774–775 carbon-14 spike was an increase of 1.2% in the carbon-14 content of tree rings during the years AD 774 or 775, which was about 20 times higher than the normal rate of variation.
A somewhat convoluted way of saying that the increase was only 1.2%, but this was an uncommon variation (a spike) as most of the time (year to year)(?) variations where 20 times smaller.
Without delving into the mechanics of possible transfer functions and localised concentration for other reasons and just going for a simple linear coupling ... this could simply mean that 1.2% more material was raised up or that 1.2% more cosmic rays were being let through ... and that this unusual (like an eruption, like field lines hiccuping, like a flare or a nova) as "normally" you see a much smaller variation in isotope levels.
Now the paleomagnetic record isn't continuous and year by year globally complete, it's formed from spot observations of the magnetic orientation at ground level in rock flows as they cooled. Inference of field strength at ground level from this is difficult, and inference from that to field orientation a few kilometers overhead is, umm, akin to reading tea leaves.
The IGRF (International Geomagnetic Field) is a richly structured and constantly fluctuating 3D beast that pulses on a daily basis and can only be coarsely approximated with confidence over five year intervals (the spherical harmonics used for this are fun).
> but just because scientists don't explicitly say "we've considered alternate explanations and found them less likely" doesn't mean they haven't done that.
A moot point as nor does it mean they have; what we have is mainstream reporting on the speculations of those scientists that are hypothesizing on the assumption that increased isotope production was caused by an increase in external cosmic ray levels.
There are possibilities that arise from the assumption of no such increase that are equally interesting and have similar probabilities (ie equally difficult to quantify)