That was absolutely true. There were many men trapped, particularly in the Oklahoma, which capsized within 15 minutes of being hit for the first time. Exactly how many men can't be said for sure. Over 400 officers and sailors were listed as dead or missing in her wreck, and by the time salvage operations progressed far enough to find bodies, they'd been underwater for as long as a year. That makes cause of death an impossibility to judge; there just wasn't enough left to tell.

Now for the good news. Rescue efforts on the capsized Oklahoma began even before the Japanese raid had ended. USS Maryland, moored inboard from Oklahoma and thus shielded by her, was almost totally undamaged. Her crew immediately set to work on locating trapped sailors via the banging coming from the inside of the ship. The truly difficult part came in getting to them without accidentally killing them.

To do this they had to cut through the steel hull of a battleship using torches, impact hammers, and metal saws. Apart from the difficulty of doing that, there were the twin worries of air loss and fire. When you cut a hole in a capsized ship, you let trapped air out, raising the water levels and potentially drowning the very men you're trying to save. To complicate matters, fuel was stored in tanks along the bottom and sides of the hull, and one cut in a bad place could easily start a gigantic fire. With skill and luck, rescue crews made up of both civilians and military managed to pull 32 sailors out of the Oklahoma within 24 hours.

Sadly, it's probable that others were not as lucky, but as mentioned before, it's impossible to know. We do know that on the West Virginia, three sailors survived for 16 days, trapped belowdecks with emergency rations and fresh water... we know this because they left hash marks on the wall of their room denoting the days. Sadly, they were found nearly six months after the attack, when salvage and recovery for that ship progressed far enough.

recommended readings:

At Dawn We Slept - Gordon Prange (old, but still worthwhile)

Descent into Darkness - Edward C Raymer. Raymer was a lead diver during the salvage operations, the book explains a lot of what needed to happen to rescue men or resurrect ships.

Pearl Harbor: Why, How, Fleet Salvage And Final Appraisal by VADM Homer N Wallin. Then Captain Wallin ended up in charge of many of the vessel recoveries at Pearl Harbor; where Raymer goes inside the ships, Wallin talks about what went into getting men like Raymer to that point.

Trapped at Pearl Harbor: Escape from Battleship Oklahoma by Stephen Bower Young. Young was one of the 32 trapped men rescued from the Oklahoma. The book is his story of that time.