Instead of going deeper into this fact --to show "how to think about claims of conspiracy"-- Professor Mcadams simply used it as evidence of a " Clueless J. Edgar Hoover " and against the hypothesis of Oswald's impersonation without inferring to the best explanation through some good arguments:
The own CIA Mexico City Station History refers it as "the best in WH [Western Hemisphere] and possibly one of the best in the Agency. [Its] technical facilities and capabilities were described as extraordinary and impressive" (page 45). Its two phone tap operations were LIENVOY and LIFEAT. The former focused on the Soviet bloc's and Cuban diplomatic compounds (page 104 ff.).
In August 1963, the monthly operational report for LIENVOY included the protocol for exploiting info (page 3): "The outside staff agent, Arnold AREHART [Charles Flick], has instructions to alert the Station immediately if a U.S. citizen or English speaking person tries to contact any of the target installations [by] a telephone call from outside the tap center at a pay phone to Robert B. RIGGS [Anne Goodpasture] inside the Station (") RIGGS meets AREHART within fifteen minutes at a pre-arranged downtown location and receive the reel with an extract of the pertinent conversation. This reel is then taken to the Station and given to the case officer responsible for the target the person was trying to contact. Headquarters is notified by cable of the action taken. Only in rare cases is information on a U.S. citizen passed without prior Headquarters approval."
By the time of Oswald's visit to Mexico City, LIENVOY had intercepted three Cuban lines: Ambassador (14-42-37), Chancery (14-13-26) and Commercial Office (25-09-14) , and five Soviet lines: Commercial Office (15-61-07), Soviet Film representative's (15-12-64), Military Attaché's (15-69-87) and two consulate lines at the Chancery (15-60-55 and 15-61-55). From all of them, LIENVOY recorded the dialed digits and audio for outgoing calls and just audio for incoming calls.
At Russ Holmes Work File ( NARA 104-10413-10074 ), the September 27 -- October 1, 1963 LIENVOY transcripts [in Spanish and some in English] show five taped conversations linked to Oswald [emphasis added].
Page 4. September 27, 16:00 hours. Phone number: 15-60-55. The Soviet Consulate received a call from the Cuban Consulate (Sylvia DURAN) who said she had there a U.S. citizen who had requested a transit visa to Cuba because he is going to URSS (") [A] Soviet tells her to leave her telephone (number) and her name and someone will return the call. DURAN gives her name and phone number 11-28-47.
Page 17. September 27, 16:26 hours. Phone number: 15-61-55. A Soviet calls from the Soviet Embassy Chancery to the Cuban Consulate and asks for Sylvia DURAN. He asks DURAN if the American has been there.
DURAN: Yes, he is still here.
SOVIET: According to the letters that he showed them from the (Soviet) Consulate in Washington, he wants to go the URSS to stay a long time with his wife, who is Russian, but also the answer had not been received (") This man (the American) showed him a letter in which he (the American) is a member of an organization in favor of Cuba and said that the Cubans could not give him the visa without the Russian visa"
DURAN: [H]e doesn't know anyone in Cuba and in that case it is very difficult to give him a visa [and] neither can (the Cubans) give him a letter because they do not know if the visa will be approved"
SOVIET: Neither can I give him any letter of recommendation because I don't know him"
On the second call's Spanish transcript, the Chief of Station (COS) Win Scott noted: " Is it possible to identify? " This reaction is to be expected under the hypothesis of normal circumstances, but Scott's next move reinforces the alternate hypothesis: something anomalous was going on.