I recall the 1000 year as 1 day explanation while I was in - I recall it being a part of a WT study during the mid to late 90s.
It's based on 2 Peter 3:8, which says that "with the Lord one day is as a thousand years, and a thousand years as one day".
This is a popular quibble used to "explain" why Jesus hasn't returned yet. The WT and others will argue that when New Testament writers said that it was the "last hour" or that the end was "at hand," they were speaking in terms of how God perceives time:
"with the Lord one day is as a thousand years, and a thousand years as one day" (2 Peter 3:8).
So we are supposed to believe that God inspired certain writers to tell people that Jesus would come again someday, but he chose to do so in language that had meaning only to an omniscient, omnipotent deity.
"Soon" didn't mean "soon," and "at hand" didn't mean "at hand," as humans understand these terms, but as God understands them.
Such an explanation makes God a devious entity who chose to reveal important information in sort of a secret code that would have meaning only to an omniscient, omnipotent deity.
The WT and others may think that this quibble is a reasonable explanation for the texts that said it was "the last hour" or that the end was "at hand", but they know that it doesn't give a satisfactory explanation to the passages where Jesus said that he would return before his generation had passed away, and so they resort to all sorts of speculative interpretations to make these passages not mean what they clearly say.