I believe from my experience and reading that oxidation from racking is a risk - just that, not a certainty. I rack every beer to bulk prime and used to rack every beer to secondary. Cardboard was not a regular flavour I encountered. Be aware though that cardboard is only one symptom of beer staling.
Oxidation and staling in beer is inevitable - it's just the rate at which it occurs can be accelerated or encouraged by various practices. Storing beer warm for lengthy periods is as much an issue as agitation and if you rack gently, you should be no more likely to get cardboard than most.
Some oxidation/staling products even have desirable characteristics in the right beer given enough time.
Anyway oxygenation and oxidation are different things.