Similar charges were made in an attempt to derail John Bolton's nomination as US ambassador to the UN as I recall, charges that proved to be bogus.
I don't know about the British Navy but in the U.S. Navy a Chief Petty Officers report or testimony would carry significant weight especially in a court martial proceeding. Here there is a CPO and a Commissioned Officer making the complaint. Looks solid to me. In short CPO is senior enlisted rank. Chief, Senior Chief, Master Chief E-7, E-8, & E-9 Ranking.
Sub duty has no room for loose screws popping off with unwarranted or in certain conditions even warranted outburst that includes the CO. If the C.O. had to do this daily then HE had a problem in his leadership skills. I worked for some rather blunt officers in my time but one screaming like Sgt Carter to Gomer Pyle in someones face on a routine basis stops in basic training. If the C.O. had issue with the officer it was his choice to keep him onboard or not. If the LT was such a screw up any Captain would boot him off first port of call especially on a sub. There is no room for screw ups. So again this reflects on the Captain although the Brits may have different regulations.
US Navy Subs have what is called a psychological & behavioral standard. If you don't meet the standard whether you are a Seaman Recruit or the Captain you can have your Dolphins taken away meaning no more sub duty. Subs at least in the US Navy is good duty. A good Captain can give you a dressing down, accomplish his goal, and not effect morale of the ship in a negative way.