Are you concerned about the word "other?" Section 223(f)(5)(A) simply refers to a rollover to "a health savings account" without any distinction between the HSA from which the distribution was made and any other HSA. Just like an IRA, there is no tax-code restriction against rolling a distribution back into the same HSA. A particular HSA custodian's HSA agreement might prohibit the HSA from accepting rollovers (which would be highly unusual), but that would prohibit that HSA from accepting any rollover, not just the rollover of distributions made from the same HSA. Even if there was tax-code restriction on rolling back to the same HSA, nothing would prevent one from opening a different HSA and completing the rollover (which is why it makes no sense to have such a restriction).
Also note that Pub 969 saying "other HSAs" makes no statement regarding the same HSA. Just because you are permitted to roll over from other HSA, doesn't mean that you are not permitted to roll over from the same HSA.
