That is not so; the CC0 explicitly states that patent and trademark rights are not waived.

Contrast that with, say, the Two-Clause BSD which says "[r]edistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met [...]".

Since trademark and patent rights are not mentioned, then these words mean that even if the purveyor of the software holds patents and/or trademarks, your redistribution and use are permitted. I.e. it appears that a patent and trademark grant is implied if a patent holder puts something under the two-clause BSD. Or at least you have a ghost of a chance to argue it in court.

Not so with the CC0, which spells out that you don't have permission to use any patents and trademarks in the work.