A number of issues factor into the perception of what a kilobyte is and how to word it.
The IEC standard names are useless: As Jeff Atwood notes there is simply no industry acceptance of KiB/MiB/GiB. Hard Drive manufacturers and Macs are the only major players using the 1000 bytes definition and Hard Drive manufacturers have absolutely no incentive to differentiate KiB from KB; it makes their drives sound smaller. Macs and Windows have no incentive to use KiB because it's an unnecessary complication for the user. Note that it's been 12 years since the definitions were created, and they're not being adopted anytime soon.
Windows Vs. Mac: Mac thinks (kilobytes are) different. If detecting the OS is a possibility, display a Kilobyte as what the user's OS would. If you can't, the 1024 byte defintion is a good fallback, seeing as 90% of general users are on Windows. Of course your target market might be different.
Scale: The problem with the binary prefix vs the SI prefix is that as the numbers grow, so does the difference between values. Once you get into the Gigabyte range the difference between GB and GiB is substantial--many Windows users are quite disheartened to find their 1 Terabyte hard drive is only 932 Gibabytes in Windows. In my experience, most of them assume Windows is correct rather than the Hard Drive manufacturer--and they have a point, it is in the Hard Drive manufacturer's benefit to use the smallest possible measure for a kilobyte.
Enterprise or Technical users are a special case. If your app is measuring disk or database usage on a server farm, that 8% difference for a GB is huge, and you should allow the user to specify how you display kilobytes, even including a KiB option. These are probably your only users who would care enough to differentiate.
Finally, let's assume people really do all think 1000 bytes is a kilobyte, in their heart of hearts. Since they know file size from what their OS reports, not from counting the bytes manually, using the uncommon 1000 byte count will add unnecessary complexity and your app will look wrong because it conflicts with what the computer says. Users only know how big a file is because their OS tells them.