It's also nonsense, I think, simply because at the time of Homer it is widely understood that nearly every Greek region had a calendar that had twelve periods for the year. They generally differed in naming of the months, and in when the year started, but they were otherwise broadly consistent. Further, there are too many other occasions in the Odyssey that refer to a year for it mean anything other than what we might recognise as a year. The more obvious conclusion is that the author has simply misinterpreted Homer's verse. First, even using the interpretation the author wants to use, if the fourth year came and seasons started again then surely our year lasted only three of theirs (such that in the fourth it was repeating the first in terms of seasons). But a simpler explanation is that the mention of seasons was indicating what part of the fourth year was being referred to.