Not true.
According to this rule, supporting points exist after release, and that's the source of this argument.
However, I'd like to point out that while arguing the semantics of the putting rules, we are forgetting their purpose. As I understand it, the purpose of demonstrating balance is to show that the putting motion is completed before the player can advance past the marker disc, unlike throws outside the circle when the throwing motion can be completed past the marker (although the disc must first be released before supporting point contact).
I suppose the reasoning behind this distinction is to avoid the equivalent of a "slam dunk" where the player takes a run-up, and leaps into the air to get closer to the basket. This means the argument would be whether the player's foot (point of contact) was behind the marker ate the time of release -- the jump putt argument).
If that is true, then forcing the player to demonstrate balance after release is an effective deterrent, and provides sufficient latitude for reasonable interpretations regarding whether the putting motion was completed or not.