The verb belie means (1) to give false representation to, (2) to show [something] to be false, or (3) to contradict. Some writers, possibly confusing belie with betray, misuse belie to mean almost the opposite of what it logically means. For example, betray would make more sense than belie in these sentences:
[W]e claim that we want Jesus to remain “the reason for the season,” but our actions belie a different focus. [Huffington Post]
Devlin points to a number of lyrical inaccuracies in the transcription of the songs, some of which belie a lack of cultural knowledge or context. [The Economist]
It is one of a growing number of social and economic problems that belie the separation of the world into developed and developing. [Guardian]
These writers use belie in its conventional sense:
Katy Perry stole the show, using her ditzy persona to belie the whip-smart pop sense of her glitzy production. [Boston Globe]
Statistics for the past two years seem to belie the opinion of some “experts” that the recession is over. [North Fork Patch]
Assistant Dean of Student Life Susan B. Marine … says that the recent incidents belie a generally positive community setting. [The Harvard Crimson]