Even if there is no direct quote of Lee saying "This is the one unique move of God on earth today", he said this kind of thing in so many words.
Here's some quotes from that one web reference at http://www.letusreason.org/cult12.htm
The local Church (Witness Lee)-
"When we were in the denominations, we were blind. I do not believe that any dear Christians who have really received sight from the Lord could still remain in the denominations. Everyone who sees must leave the fold and enter the pasture, under the sunshine, in the fresh air, in liberty. Where are you now? Are you in the fold, or are you now in the pasture? Allow me to say this: if anyone is still in the fold, he is blind. Of course, a blind person requires the fold to keep him. But when he receives his sight, he will swiftly leave the fold for the pasture, for the sunshine, for the fresh air.”
(Witness Lee, Christ Versus Religion LSM, 197,1 p.109-110)
"The only way to follow the Lord absolutely is to go the way of the local church."
(Witness Lee, The Practical Expression...p.94)
"If you leave the church (the Local Church), you miss the mark of the Lord's testimony. You must be in the testimony of Jesus. Only the golden lampstands, the local churches, are the testimony of Jesus....if you are not in the local churches you are not the testimony of Jesus.”
( Witness Lee, The Stream magazine Nov. 1976, p.7)
Though these are older quotes, Witness Lee never retracted or repented of saying these things, and they are very representative of what the man taught throughout his ministry here in the USA. He clearly implies that his little sect is "the pasture", and all others are blind sheep in the fold. No wonder the Local Church got tagged with the "cult" word early on. Then to add insult to injury he says the only way to follow the Lord absolutely is to become a member of the religion he invented....how convenient! And to top it all off he just can't resist threatening his followers with missing the mark of the Lord's testimony if they decide to go to some other church. Yes, Lee implied that The Local Church was the one unique move of God on earth today.