You are right in that a cut flower is still a living thing, up until the stored
energy in the stem is used up.
To take it farther, as the other reply stated, some plants root more freely
than others, but even within those varieties, there needs to be a node on the
stem of the flower. A flower cut above a node is not generally going to root,
it will gradually wither away, but if if there is a node on the stem, it may
root. The flower itself will wither back to the node, and the node will send
out a new plant.
Depending upon the specifics of your bet, you both have a valid point.