All four of your simplistic rules fail when applied to actual humans in the actual real world, although it may apply to a world of homo economicus i.e. a world of identical sociopaths. It ignores any number of irrational behaviours that people's brains are wired for, ignores any effect of risk, ignores any effect of altruistic behaviour, ignores any long-term planning or perspective (even a sociopath might consider reputation and consequences!), ignores the many cultures where gift giving and receiving have been hugely important, and in fact ignores circumstance, context and individuality at all!
And saying people will be more careful with their own money is not even necessarily true - a lot of people would be much more careful if looking after say their friends' money than their own, especially if you're bad at managing finances! How much care they spend on other's money depends on a number of variables, including how close they are to the money's owner, the consequences of failure, the chance of failure and the amount of money itself. There's been a ton of research on these questions in the field of behavioural economics recently, and the answers aren't as simple as "people are rational narcissists".