The correction is correct, albeit a bit pedantic, given the point of GPs comment.
(but that explanation also glosses over the fact that containers are something else entirely... "data format" may be better than "file format" here)
Implementations and encoders actually use algorithms to turn the media into something that is compatible with a codec.
But how can an implementation be compatible with a codec, if a codec is not set in the stone -- i.e. if there are different versions of a codec?
Obviously encoders are constrained by the fact that they must produce a series of bits that can be decoded according to a certain standard, so a new video format can enable encoders to compress information more efficiently (i.e. less perceptual loss of quality at the same bitrate).