The Free Software Definition doesn't require free software to be copylefted or to include measures against TiVoization or against proprietary or restrictive downstream products. GPLv3 does this and the BSD license doesn't, and both are free software licenses.

As I said in another comment, people who usually say "free software" are more likely to think that preventing restrictive downstream products is an important goal than people who usually say "open source". But that doesn't mean it's part of the definition of what it means to be free software.

EDIT: I also think the comment the parent replied to was right to say "then the whole is not open source". BusyBox is both free and open source even though its license allows it to be included in the locked-down TiVo -- but the TiVo as a whole is not open source.