LivingDNA claim about percentage range of DNA inherited from a grandparent

[TopLobster]

In the "Family Ancestry" section under the "How the science works" sub-header, the following is written:

"If your grandmother was 100% Eastern European and the rest of your ancestors came from Asia, then your genetic profile could contain anywhere from 0% to 34% Eastern European."

How accurate is this statement?

According to this Razib Khan article, there is a 1 in 4 million chance that the chromosomes inherited from one parent could come entirely from just one grandparent, but are the typical ranges of DNA inherited from each grandparent for the vast majority of people very close to 25%?
http://www.slate.com/articles/health...y_related.html

[unorigional]

Well, technically if she were your maternal grandmother that statement would be wrong. But even without that catch, it would be very unlikely, as Razib stated. But, a 1 in 4 million chance, taken over 7.6B people means that it likely has happened.

The Shared cM project (https://isogg.org/wiki/File:Shared_cM_version_3.jpg) lists the average number of centiMorgans that a person would inherit from their grandparent is between 1156-2311cM with 1766cM being the mean value (~25%).

[Maciamo]

Statistically there may be one in 4 million chances of inheriting all of one grandparent's DNA and none from another. However I am not sure it ever happens in reality, probably because of still unknown processes in the way DNA recombines. I have seen dozens of 23andMe results of people who tested their grandparents and most of them are very close to 25% from each grandparents (typically between 22% and 28%, but often between 24% and 26%). I think that the lowest number I have seen was 20% from one grandparent. Now dozens of families may not be much. But over a million people tested with 23andMe and searching a bit online I have not found any body reporting less than 20% or more than 30%.

I don't know of any study that investigated the actual inheritance percentages one a large scale. Biology is not mathematics and we should be careful before assuming that because something could theoretically happen based on statistical calculations it will really happen in nature. There may be biological mechanisms that keep some checks and balances on the proportion of DNA inherited across more than one generation.