Can a CFI provide endorsement training to non-US citizens without TSA approval?
Assuming the crux of this question is about the need for TSA clearance for the training then the answer can be found in the FAQ section of the flight school candidate website under the question;  When is a flight student exempt from the requirement to undergo a TSA security threat assessment? 

You will see a table with some exemptions including the 14 CFR §61.31(g) exemption. The table is prefaced with the statement;  


  Other training activities that do not require notification to TSA are
  exempt only if the candidate holds an FAA stand-alone Pilot
  certificate


In other words a pre-existing FAA pilots license acts as some what of a verification and you do not need to be re-verified. 

Interestingly only 14 CFR §61.31(g) is exempt so presumably only the high altitude sign off can be obtained under this exemption the rest of 14 CFR §61.31 does not fall under it. I would say the AOPA site is incomplete in their information.  A CFI may provide training for 14 CFR §61.31(g) without TSA authorization but if the student is seeking training on any other endorsements under 14 CFR §61.31(g) then they must get cleared by the TSA.