For example: "New Jersey’s civil union law harms children, says court brief." From this, one might think the legal brief in question claims that New Jersey's legal civil unions, in and of themselves, harm children. However, the main point of the actual court brief seems very different: "Children of Same-Sex Couples Are Harmed By The State's Decision To Deny Their Parents The Right To Marry." Tack on "says court brief" at the end, and ADF could convey the brief's True wording and still fit it all within 140 characters.
If the ADF's audience were expected to read the actual brief—or even the excerpt from the brief displayed on the ADF's own website—then the title of the alert might seem innocuous. But as a single-sentence message sent to presumably busy people—who might only remember the meaning conveyed in 140 characters or less—the alert sends a very different message from the true legal brief it cites.
Now, this might not be considered outright lying, but it certainly seems deceptive—which is quite an irony from an organization declaring itself dedicated to "defending the right to hear and speak the Truth."