White Space Broadband = no TV
They can't avoid interfering with TV. First, TV tuners have relatively wide front-end filters. So it's not just devices on the channel which cause problems, it's adjacent and in come cases 2nd adjacent channels which cause problems. You can get away with 1st adjacent if the transmitting antennas are co-located and the power of the signal is similar, but that's simply not true with white space devices.
Second, people in these rural areas where this white space broadband stuff is proposed often need to use a pre-amp to get their TV reliably. A pre-amp amplifies across the whole band (or bands). A nearby white space transmitter anywhere within the band will overload the pre-amp and result in loss of reception.
It's just not feasible to run white space devices in the same spectrum as the current TV infrastructure without degrading the latter significantly.