[kadoban]

As always, it depends on your computational model. People are awful at specifying a model, in other words it's unclear what's even being stated.

You can compute the nth fibonacci number in O(lg n) additions and multiplies. That indeed doesn't turn out to be a good model for how long it takes on an actual computer though.

[madez]

And even if the model is sufficiently specified, the constant factors and lower terms hidden in the O-notationen can be deciding in practice, and are yet usually left out.