This might be a bit strong. Perhaps "Naive Programmers cannot be trusted to use computers to do arithmetic." :-)

If you are aware of the limitations based on how the hardware, libraries, and language does arithmetic (iow - know your tools), computers can be used to do the job just fine. I had two courses in this in college that dealt with this topic - one in the math department and one in the CS department. It is a similar concept to students writing down a highly precise, but terribly inaccurate answer on a test because they didn't understand significant digits and error accumulation.