That is correct, but they are just praying that the computer does what they want, and does not suddenly mess up their data because a bit flipped in the memory. It does not happen often, and it does not always have disastrous undetected results. Probably more often it just makes your program crash with one of those "Microsoft Outlook has stopped working, click here for details" messages boxes that people click away without even reading them. But in some cases it may result in a wrong letter somewhere in an email, that you later attribute to a typing mistake.
You can be sure that Amazon and Dell themselves do not trust their company data to systems without ECC RAM. It is your own decision if you want to do the same.