This is (and has always been) false. We could, if we wanted to, reduce all long-lived (say thousands or more year half-life) isotopes to hundreds of years or less by neutron bombardment (pick any of a number of sources). The cost would be tremendous, so we usually don't talk about it aside from a few academic studies.
Nuclear power will produce waste, and that waste will ultimately need to be dealt with. I think non-permanent burial is the best option because in the future reprocessing will be much more economical. But there will be some parts that are always trash, like most other things we humans use that produces trash. But compared to other big energy producers, the trash nuclear plants produce (including emissions, mining waste, spent materials) is amazingly small. To go to a nuclear plant and see, for instance, all the spent fuel of decades of operation standing in a few casks is impressive. Nuclear's advantage is so much energy contained in a small fuel form. At the back end of the process that means the most radioactive waste is also contained in a very small form.
We are smart enough to hold it somewhere safely. I'm sure in the near future we will be even better equipped in ways we can't imagine, but I think today's tech is adequate. This doesn't mean we can't deal with it, or should stop thinking of how to improve waste management, that means we *are* dealing with it.