Oxidation of beer will not occur with a slight bit of swirling, or even stirring if it becomes necessary (such as in stuck fermentations). Simply removing your bucket lid or carboy cap is not going to oxidize your beer. You defintely need to be careful with splashing, anything that causes bubbles can introduce oxygen into your beer.
As Mad Milo states, there is a blanket of co2 over your wort/beer, and usuually this is protecting your beer from oxygen.
As Revvy states, unless you were to unload an entire dispoable red oxygen bottle into your beer, you needn't worry about oxidation.
I won't say it is a myth, but it is highly unlikely that you will have any oxidation issues. Having said that, oxidation becomes a problem with storage. Most will probably drink their beer long before off-flavors from oxidation will occur.