Gasoline is an organic solvent also, and, if you own a plastic gas can, it is almost surely HDPE.
Benzine may dissolve PE as suggested in the article you linked, I don't know that for certain. But, we used to store 95% and 100% alcohol in HDPE in our labs for extended periods of time, and all three of the bottles of 91% and 70% rubbing alcohol in our house are HDPE, all the bottles are years old, and there is no sign of damage. As for acetone melting PE as suggested in the linked article, it might, under some circumstances, but my wife's fingernail polish remover (yes, it is acetone) is in the same HDPE bottle it was purchased about 5 years ago and again, no apparent damage or obvious aging of the bottle.
Also, for what it's worth, many wineries ferment their wine in large PE tanks as standard practice.
HDPE is really amazing stuff. I would not be the least bit concerned about storing alcohol in it.
I just hunted down
this table that may put your concerns into context.