While you do own the copyright whatever you do with the license, if the terms of the license aren’t made to legally apply, then the legal rights of the recipient could turn out to be very different than what the license says.
If you want to have a very high degree of confidence that the terms of your license will be legally binding on the recipient of the code, you should have a process in place that requires them to signify their agreement to the terms before they get the code (for example, the usual “click here to agree” and if they don’t click, then no code is delivered). Without something like that, they MAY be bound to those terms, but it will depend on a variety of other issues their lawyer would point to if it ever mattered.
There are many circumstances that may make it matter – here are three of them: If you want to be able to use legal process to collect money from the licensee (presumably not your situation), if you are concerned about getting the licensee to agree not to hold you liable if the code doesn’t work, and if the code actually belongs to a third party who requires you to apply their terms.
Obviously, you should talk to a software lawyer for advice in any particular case. Point is, just doing what Apache says may or may not be enough to cover all the legal issues.