Charity Engine is based on Berkeley University's famous BOINC software, which has been safely running on over 6m home PCs for the last 7 years (as used by SETI@home, the BBC's climateprediction.net, etc).
BOINC doesn't 'take control' of a PC, that's not how it works. Instead, it asks our servers for a work unit - part of a giant computing task - for the PC to work on in the background. When the PC is finished, it uploads the answer and gets another work unit.
And that's all it can do.
BOINC tasks cannot even see what's on a computer, nor interfere with it in any way. The source code is open-source and public, so anyone can check it - and the guy who wrote it is working with us.
(For the technically-minded, Charity Engine source code can be found in the BOINC source code repository.)