Even mixing 1060(1070) + 1080(1080ti) is not good idea.
They have different hashrate in different algs and it would be a pain to make maximum profit with them combined.
This statement is just bullshit. I have been running a rig with 3 x 1070s and 3 x 1060s for a few months now in Windows 8.1. It will happily mine ETH using Claymore at 170mh/s, using about 780W for the whole rig.
I have also briefly tried it mining zcash with EWBFs miner and it was no problem.
I have also run AMD rigs with older AMD cards using the Ethos custom linux distro. I have run a rig with 1 R9 390, 1 R9 380, 2 R9 290s and 2 R9 290Xs. No problem.
So yes you can mix up the different cards, but it's much easier if you use the same brand (AMD or Nvidia) and it's much easier if they are from similar generations. It is however possible to run rigs with different brand cards. One proof of this is that there are a few manufacturers out there releasing motherboards with crazy numbers of PCIe slots. Given that the drivers for AMD and Nvidia both currently limit maximum number of cards - if you got a motherboard with 13 PCIe slots - you would have to run for example 7 Nvidia cards and 6 AMD cards ON THE SAME MOTHERBOARD. You would probably have to run 2 separate instances of mining software - 1 for Nvidia using their driver and 1 for AMD using their driver, but they wouldn't make these crazy motherboards if it wasn't possible.
So my point is -of course it's possible. Might not be easy but definitely possible.