I think that statement does explain it pretty much. Keep in mind that eimi means "I am" or "exists". With that in mind read into Matthew 13:40 exists instead of "will be". It makes as much sense and doesn't corrupt the original meaning of the Greek word. It would read like this.
Matthew 13:40 "As the weeds are pulled up and burned in the fire, so it will be exists at the end of the age.
Now in verse 41 the word is apostelló or "I send forth".
In verse 42 again it could better read "where there will be exists weeping and gnashing of teeth."
Your on the right track. Closely checking the Greek and also making sure each verse works with the rest of scripture allows for much more clear understanding.