I know some dear people who have, at some point, found themselves in this predicament. In a couple of the scenarios, the search yielded nothing that was of concern. In another situation, it caused them some legal troubles.
In all of these cases, I heard them talking about whether or not it was legal for law enforcement to have done so, given that they didn't have a warrant.
Some Texans do it because they see their parents or grandparents do it. Some people say they want to wash away some of the fat--but does this process even help with such a thing?
Other Texans say it is completely unnecessary, not to mention, possibly unwise to rinse ground beef after (or before) cooking it.