I think I saw a thread on the old board discussing whether or not this was actually the case. One poster (don't remember who it was, now) saying that if this was the case, how come no one had stepped up to claim it in a "secrets revealed" sort of way. Think about it: if Hichens had turned the wheel the wrong way, the crew would want to keep that a secret, sure, but usually it's hard to keep one between more than two people, and in this case, there were 705 people who survived. Wouldn't someone have heard this and cashed in on it?
No, you are right I think, this probably was not the case. In fact, I think Lightoller's granddaughter claimed that her mother told her this, long after lights death, which makes the claim more dubious.
Having said that, it has long been assumed that the surving officers went to great lengths to protect Smith's reputation and White Star in general, and none of them ever came clean about this.
And as far as the claim by the granddaughter who would have known. The only people on the bridge at (or near) the time of the collision who survived were the QM who would have made the error and Boxhall who would have certainly lied about this to keep his job since an admission would make White Star liable for the accident.
Then who else might have been told about this after the fact? Ismay certainly who would never reveal this. Perhaps Andrews who perished and the senior bridge crew all of whom died except Lightoller.
So really you'd have to rely on a conspiracy of Ismay, Lightoller, Hitchens and maybe Lowe.
None of whom would want to share this information, at least while still working. Not only could they possibly have been found personally liable, but White Star certainly would. They would have lost their jobs and I find it very unlikely any other line would touch them--effectively ending their careers and lively hood.
Even as it played out none of Titanic's officers ever received their own command on a merchant vessel.