Banks create real money simply by approving a loan.
The intermediary "theory" is a misconception, at least regarding money creation as it works today as you point out yourself. Banks don’t lend out customers deposits. On the contrary: By approving a loan, a bank, say Bank A, creates a deposit of the same amount in the customer’s account. For all intents and purposes this deposit is already real money. In fact, this so-called broad money is used for the vast majority of transactions in a modern economy (direct debits, bank transfers, credit card purchases, etc.).
As a result of this money creation, the balance sheet of bank A grows. There is a claim on repayment of the loan on the asset side, and the liability side reflects the new deposit which A owes to the customer. But A’s reserves - the kind of money only the central bank creates, and which is used by commercial banks to settle accounts between them, remain unaffected by that process. Only when the customer transfers some of the money to another bank B do reserves come into play. A will transfer its liability (the deposit) to B and, to make up for it, it will also transfer reserves of the same amount (an asset). Although A has now less reserves, and B more, the total amount of reserves in the banking system has not changed, other things equal. So, banks can create real money (the money used in commercial transactions) simply by that process, and reserves don’t play a role in the process itself.
Effects of making a loan on balance sheets (without reserve requirements)
Source: BoE quarterly bulletin extract (2014)
However, if in place, reserve requirements (when banks need to hold a certain ratio of their deposits in reserves or cash), do limit the amount of money that can be created, but are not involved in the process of how money is created by commercial bank. Reserve requirements, even if they exist, have become much less relevant over time, partly because of securitization (of loans/deposits, think about lowest-quality mortgage securitization ahead of the financial crisis), which allows them to restructure their balance sheet in favor of more reserves.
That doesn’t mean the central bank can’t steer the creation of money or do it itself. On the contrary, monetary policy is all about balancing the relationship between inflation, money supply, and interest rates (the price of money). And of course, the central bank can affect the amount of money more directly via quantitative easing, but that was not the question.
Capital requirements are designed to curb systemic risk and, possibly, to limit the speed of money creation. If a bank accumulates profits into capital, it can still grow its deposits and hence create ever more money, the speed of which is only limited by the speed at which it can grow its capital.
What will limit the amount of money that is created are the banks’ profit considerations in the context of competition and macro-prudential regulation. You could argue that banks can, and do, create money out of “thin air” when they approve unsecured loans (credit card debt, overdrafts), because there is no collateral backing it up. But in many cases, especially for larger loan amounts, banks will require some high-quality collateral to approve a loan (for example the rights to the home for a mortgage loan).
As banks increase their loan portfolio, remaining loan opportunities will eventually become too risky relative to interest rates banks can charge in a competitive environment (or, in other words, borrowers as a whole run out of high-quality collateral). At that point banks will stop lending and, hence, stop creating money. Note that this risk is perceived risk, and money creation by commercial banks will ultimately depend on how they perceive risk. Macro-prudential regulation, such as caps on loans-to-value ratios impose limits to the risks banks can take from the outside, and hence limits money creation in that way.
If an individual person were granting a loan it would be different for a variety of reasons. Most importantly, unlike banks, you don't have access to reserve money and cannot borrow reserves from other banks or the central bank when people actually want to see their money right away, which will always be the case in that situation. So, you wouldn't be able to create money.
References (all focusing on the UK, but most mechanisms are general):