That's interesting. Anyone living near the relevant Archive could look up what the crime was exactly, provided the sailor under discussion was discharged (with sentence served) before 1950.
I am completely certainly certain that the ship's logs are not the court records.
Also, I went looking for access to Deck Logs' availability. They are NOT sealed for a set number of years, but are now under the Freedom of Information act. They do charge for the cost of duplicating any records you ask for copies of - 15 cents a page for paper record, 25 cents for a microfiche sheet.
The Navy itself keeps the deck logs for 30 years. At age 31, the logs are transferred to the National Archives. There, old logs (1775 thru 1940) are housed in one building in DC, and newer logs in another near DC. (They probably filled the first up completely.)
Any requests for logs within the last 30 years: "If you notify Navy FOIA Office you are willing to pay for the reproduction of the deck logs then your request will be forwarded to the appropriate Atlantic Fleet or Pacific Fleet command for review and final release determination of those specific deck logs you have requested." In other words, some of the newer logs may be classed as secret for security reasons.
I don't think this includes Coast Guard vessels, but their security is probably the same.