Did he (the author) specify the position of the caller? We have 3 pretty different ranges between BTN-SB-BB, so we should probably play a different strat vs each range (in terms of what combos we cbet/check back.)
The strongest* of the 3 prospective ranges here would be SB, who will have the largest proportion** of sets and combo draws. BTN's range could be similar with respect to nut/high equity hands but overall should be much wider. BB will be by far the widest range and thus will have some additional 2pr and str8 combos that SB and BTN cannot. BB will have the largest amount (but smallest proportion)** of nut/strong hands.
*strongest defined as having the largest proportion of strong hands.
**proportion=percentage of entire range.
Here's a GTO strat vs a BB Range:
Disclaimer: I'm not a GTO expert but I have looked over a few sims...
CO Opening Range:
Flop: Overpairs check back mostly b/c BB has > 2pr+ hands on this board. JJ and TT check back much less (than QQ-AA) b/c they need more protection.
Turn: Becomes an Easy Call after checking back OTF...AA still ahead of some value and BB can have a lot of semibluffs.
River: GTO strat will Call most AA combos vs. the overbet (it calls ~100% AsAh b/c that combo unblocks the most bluffs.) As you can see in this sim, the author's combo (AdAc) is mostly a fold. This doesn't mean AdAc is a bad/losing call (vs a different BB strat), it just is part of the distribution that GTO uses to arrive at the correct calling/minimum defense frequency (~36%.) For example, if you decided to call all AA combos and fold erry KK combo (except KsKh) you would be at virtually the same calling frequency and I doubt if it would affect your overall EV much.
Please refer any GTO specific questions to Eggs or someone more qualified than me...I only used the sim to demonstrate a strat that checks back a lot on the texture in your example.
To answer some of your questions RE specific hands and why they check back, it's probably easier to just focus on AA. One reason AA is a great hand to check back is that it requires the least protection since it's not vulnerable to overcards. Although AA has good equity vs. a BB range (def good enuf to cbet for value) checking it back also can induce more bluffs.
It's ok to sacrifice the EV we get from cbetting in order to strengthen our check back range, which is just another way of saying we are increasing the EV (of calling bets on future streets.) Vs. aggro/bluff-happy opponents, the EV of checking back can be >> EV of cbetting.