To some degree all plastic is permeable to O2, _BUT_...
In general, the primary fermentation stage is too brief for any
significant oxidation to occur. You get far more O2 infused during
the siphon process to get the wort into/out of the primary than you
would through the walls of the primary. I've even seen commercial
brew-pubs add a polyethylene primary fermenter when they needed to
quickly extend their capacity.
Use of plastic soda bottles for final bottling may be the source of
this. They are much thinner than fermentation buckets, and the
product sits in them much longer.
You'd think the pressure of the CO2 would keep the O2 out, but
actually the infusion rate vs. partial pressure of different gas
species is almost independent.
Verba Movent - Exempla Trahunt
Words move people, Example compels them
Godfrey Thacker of Northumberland.