Another possibility revolves around timing.
After this trade, the Bengals have two QB's and they seem to have adequate cap space. The news media speculated that Finley was going to be released. But when? The Bengals may very well have carried him into camp and released him later.
It's to any teams advantage, especially when in a rebuild, to have players, especially QB's, signed and participating in all the pre-camp programs. The Texans obviously liked this QB and wanted him on board sooner rather than later.