More shares mean less volatility because it takes a larger number of trades, a larger number of shares per trade, or a combination of both to raise or lower the stock price.
Institutional investors (mutual funds, pensions, hedge funds, other investment firms, etc) are the sorts of organizations with the large amounts of money needed to move a stock price one way or the other. But the more floating shares there are in a company, the harder it is for one or two firms to move a stock price. A company with fewer floating shares wouldn't require as many trades (or as many shares per trade) to see wider swings in price.
When it comes to stock price, insider trading isn't the same as manipulation. In the (surprisingly few) cases of insider trading that are prosecuted, it tends to be an individual (or small group) with early access to information that the broader market doesn't have being able to buy or sell ahead of the broader market. Their individual sales are seldom if ever enough to noticeably move a stock price. They're locking in profit or limiting a loss. Manipulation might (but doesn't always) precede insider trading, if misinformation (or truth) is released for the purpose of creating a situation that can be profited from via a trade or trades.