That can only be described as outright lying, or the person saying it is completely without any knowledge. In both cases they have no right to be saying it. Exactly the opposite is the truth.
"very unstable and speeds with drasticly decrease in peak times". Isn't that what all the complaints about BT in that forum here are all about?
The truth is that O2 offer two services - LLU and BT based. The BT-based one is dodgy.
The LLU one is excellent. All the reports you will see on here from O2 LLU users (barring genuine faults) are that their download is over 80% of their connection speed 24/7. The maximum possible is about 85% and most of us get over 83% nearly all the time.
Equally as good is their sister company Be. I believe also good are Sky/UKOnline/Easynet. TalkTalk is good for mass market such as BT serve - where no great performance is required.
C & W LLU through resellers such as vivaciti, xilo and aquiss are apparently more than satisfactory, though perhaps not through Demon.
Orange LLU some people report good, many report bad. Tiscali and its subsidiaries are dreadful by what we see here.
So with regard to those I suppose the person could justifiably claim that
they are no better then BT. But O2 was specifically mentioned and it isn't so.