VO2 max is also exercise dependent. If you trained riding bike for 3 months, then went to run down the street, your VO2 max would not transfer over.
You won't be a 55 Vo2 runner if you're a 55 Vo2 Cyclist, but cardiovascular fitness does cross between those activities to an extent
This is incorrect - the primary factor is heart and lung function. Yes, muscle training can play a factor, but is relatively minor compared to that.
I think the GP's comment is just easy to misread.
https://onlinelibrary.wiley.com/doi/10.1111/j.1748-1716.1976...