@Gusbrecht
Davies is not saying the inner wing reattaches. He says that the tip may stall FULLY before the inner wing stalls FULLY.
Generally it's hard to get the inboard to stall before the tip - everything is favouring the tip to go first. So the designer biases it. But there's a penalty to be paid, in performance/efficiency, in doing so. So you can't afford to totally kill the inboard wing.
So you twist and dress the wing to force an inboard stall to start. But maybe it only stalls right where you put the trip, or right at the end of the slat, or whatever; the REST of the inboard wing is still very robust. keep increasing AOA and now the tip goes; increase it more, and the tip stall develops and spreads, while the inboard still has only a partial stall.
Its all because the tip stall is "natural" and the inboard stall is "artificial" - the tip is really where the wing "wants" to stall, and the designed-in inboard tendency gets overcome by the natural behaviour.
I'd also caution that to read basic design principles - such as "don't let the tip stall first" etc. - and to ASSUME that any given type slavish follows that behaviour is dangerous. The ultimate pass/fail is whether you can comply to the relevant regs (at time of cert) - not some theoretical design goal. If I have a small tip stall first, but it doesn't grow, then that might be fine. For example, I don't think anyone deices a winglet, so chances are with ince on the airframe, the winglet (and perhaps the last few feet of the wing) stalls long before the protected portions. Not in and of itself an issue - if it passes the regs, it's ok.
edit to add that the above is intended as generic comments on the general wing design statements being made; i don't have specific knowledge of the B737 wing design nor its stall characteristics