If I had three years and unlimited patience, I might be able to assemble enough parts to build a bike for under $1000 which weighed less than 15 lbs.
I doubt it.
Where do the wheels come from? I suppose I could take the wheels of another one of my bikes and call them "used take-offs. however, i would still have to count them at full purchase price if I were honest.
I look online for wrecked bikes for parts. It seems (not a scientifically rigorous result) that most people who know enough about bikes to have really good, really light parts, know what they have and chose them and paid for them, and sell them fro good money when the frame breaks.
I have tried to by some good parts cheap ... but usually there are other folks out there who do the same thing, and at least a few start an EBay bidding war ... and there goes the budget.
I suppose it is Possible ... if someone had the patience and the luck (or a huge store of old bikes to pick through.) For most people I am pretty sure it wouldn't be worth the effort. I could save up enough money to buy the stuff new in the time it would take me to find it used, NOS, or new-take-off.
IMO.