I don't see anything about ticketing in the policy

United’s 24-hour flexible booking policy
The 24-hour timeframe begins at the time your ticket is purchased.

In the DOT prohibition on post-purchase price increases (14 CFR 399.88) they define purchase as:
A purchase is deemed to have occurred when the full amount agreed upon has been paid by the consumer.
But I'm not sure if that's the definition of purchase that applies here.