Did Trump Betray The Kurds?

It is said that after a conversation with the Islamist dictator of Turkey, Erdogan, Trump decided to remove the small number of Americans that were assisting the Kurds on the Syrian side. Trump gave convoluted reasons for his decision, including some nonsense about the Kurds not being present during Normandy.

Defense Secretary Esper said that the 50 or so Americans that were with the Kurds were pulled out because the administration knew the Turks and their allied Arab militias were going to attack, and so the Americans were taken out of harms way.

What is the truth? Did Trump's conversation with Erdogan and Trump's decision to pull out the Americans embedded with the Kurds provide the green light for the invasion, and now the administration is covering its tracks?

If Trump knew Turkey was going to attack the Kurds, then what, if anything, did he do to stop the invasion? Trump said he is a masterful negotiator. Are we to assume he could do nothing to stop the Turkish invasion, assuming he did not green light it? Or that he plain did not care?

Why did Trump decide to pull out the small number of Americans, which is now followed up with the removal of the other 1000 or so American troops working with the Kurds?

The argument that Americans must stop being involved in overseas conflicts only makes sense if there was actually a conflict. While the Americans were with the Kurds in the Kurdish controlled zone, there was peace. The American presence deterred Turkey, Assad and Russia. 

If Trump gave the green light to Turkey, then Trump and his administration bear full responsibility for the harm that is now befalling the Kurdish population, for the ISIS Islamist prisoners that the Kurds were guarding and that escaped, and for throwing one of America's most dependable allies under the bus and into the arms of the Russians, Assad regime and Iran.