That's what they think they are saying. What it actually means is "It is my mistake that I admit is mine, you get fucked, I keep my chair and take zero actual consequences for it"
If I told someone "we'll be working on this report til the cows come home", I wouldn't expect that it's necessary to explain that the expression doesn't actually have anything to do with cattle, and instead just means I'm expecting this to take a long but indeterminant amount of time. If someone found it clever to point out what I _actually_ meant, I wouldn't find their input very helpful, just socially unintelligent and annoying.
Usually it's more helpful to just research what an expression means, rather than trying to argue about what you personally think it _should_ mean.
"Taking responsibility" (taking care of the kid) of condom breaking is a bit different than "taking responsiblity" (doing absolutely nothing of substance) in corporate world.
Your observation that words being said in the corporate world may be interpreted differently than in the bedroom is not a meaningful one and just comes off as uneducated, if I have to be honest. Communication in the corporate world is often deliberately vague, congratulations on your groundbreaking discovery.