Okay, I do see some similarity. There's an equality principle
underlying both provisions.
GPLv3 section 6 states that the anti-lockdown provision does not apply
"if neither you nor any third party retains the ability to install
modified object code on the User Product".
In other words, the policy problem the anti-lockdown provision was
aimed at (by the time of its reformulation in public Draft 3 of GPLv3)
was the asymmetry of upstream (or some third party) being able to
install modified versions on the user's device, with the user being
technically thwarted from exercising a similar freedom to install
modified versions on the user's device.
In the copyleft-next provision, the original licensor is effectively
saying "If I get to create proprietary derivative works, then you
ought to have the same right to create proprietary derivative works".
There's also an equality principle underlying some of the GPLv3 patent
provisions that have no counterpart in copyleft-next.
So, yes, principles of equality and nondiscrimination are part of the
legacy of the GPL family (and I suppose FLOSS licenses generally), but
different licenses implement those principles in different ways. For
example, pure non-copyleft licenses say "everyone getting *this* copy
gets an equal right to create proprietary derivative works".