I'll repeat myself trying to be more precise on my words.
A. The catalyst says that ALL synthetics will be destroyed.
B. EDI, a synthetic, is not destroyed.
-If we assume A as truth B is impossible, the landing scene is false.
-If we assume B as truth A is a lie.
C. Word of God says that B is truth.
-B is truth then, the destruction of ALL synthetics is false.
D. No dead Geth are shown
We cannot conclude that Geth are dead, since the only premise that would lead us to believe that the Geth are dead (point A) is proven false by Word of God.
We cannot conclude that they are alive either, since no Geth are shown alive.
Data is insufficient to reach a conclusion in that regard so speculation is left open.
Assuming that they die because of a false statement is "as much fan fiction as the indoctrination theory."
Edit: That is the case only in one of several endings.