Yes they can and often do. It is illegal wash trading and many groups have been getting busted for it lately (google "Ryan Reynolds" of Dallas, for example). It is the new pet project of the SEC and the Justice Dept to bust people who wash trade. I have heard rumors that some huge new indictments are coming down before the end of the year on several big groups of wash traders.
We are apt to shut our eyes against a painful truth... For my part, I am willing to know the whole truth; to know the worst; and to provide for it. --Patrick Henry, Patriot and Hero of the American Revolution