(I assume by "sends a smart contract to some address", you mean "calls a contract at some address") Suppose two accounts, A and B, both have 10 ether in them. If someone calls a function in a smart contract according to the rules of Ethereum that, say, moves 1 ether from account A to account B, then everyone who follows the Ethereum rules will agree that account A now has 9 ether and account B has 11. If someone were to ignore the function call making the transfer, they would still think that account A has 10 ether and account B has 10.
This is fundamentally no different from the owner of account A simply modifying their Ethereum client to credit account A with a million ether out of thin air. The result is that account A has a different subjective reality than everyone else.
Why does this matter? Imagine if I, alone, believed that Canadian dollars (CAD) were on par with US dollars (USD) and I went to a US restaurant and paid with CAD at par value. The result, as you'd expect, is that the restaurant wouldn't accept my payment. The result would be very different if the restaurant also believed USD=CAD. Then they'd accept my payment, but no one else would accept our CAD on par. So this is a strong disincentive for the restaurant to believe that USD=CAD -- that nobody other than me would have that belief. They are strongly motivated to go with whatever the majority of people believe because that, all else equal, gives them the most utility for their CAD and USD. For any bounded rational thinker, this is also true. Thus, you would expect everyone to converge on one unified belief in the value of USD and CAD out of selfish reasons. See also this question for why a particular value for CAD and USD can be converged upon.