Why would the B1G or SEC feel any animosity toward the PAC, B12, ACC?  There's no rivalry there.  There's no competition.
As a fan of a B12 school watching all of this unfold over the past decade+, I never felt like the SEC or B1G felt animosity toward the B12.  My perception is, they don't feel ANYTHING at all.  It's all just business, exclusive of emotion.  Those other 3 conferences are viewed by the B1G and SEC as being solely for consumption.
But I most definitely perceive a rivalry between the SEC and B1G.  Perhaps that will stabilize and go away, once the TX/OU and UCLA/USC moves are complete and the dust settles a little bit.