Great sechel. I can add tomorrow iyh stories and a bit more more as I want to check up some points before. If you’d like to check up yourself, the answers to these and many similar questions can be found on the stump the Rabbi site, where the rabbis answer questions that are from ffb Chabad people who ask all these questions at some point.
To summarise the points flow:
1) lubavitchers understand that sicha as the Rebbe intended with his other examples, as a tzadik being a revelation of Hashem in this world, like Moshe was able to say I referring to Hashem etc.
Other sources include nefesh Hachaim which says the same thing. Any other attempt to “read” into it is taking it out of context (like missionaries do), and done to drive an agenda which isn’t there.
2) we know it’s done but why is it OK to ask Rebbeim/tzaddikim for brachos as opposed to only Hashem?
Answer because the tzadik is a mimutza hamechaber so Hashem can answer you through the tzadik. And you can put your “best foot forward” by having your “head” ask for you.