EDIT: Getting better... just reached out a rude lady: "We don't do price match guarantees here, goodbye!"

-> ...?!

EDIT 2: Finally reached a motivated agent -> was put on hold -> he searched alone for about 30 minutes under the instructions given (even on other websites, he said). Then came back to me and said he can't find the lower rate (even the room type claimed). We went through once again together and he found out he was looking for a different period... The lower price was gone in the meantime.

He did apologize and offered 5k HH points as a compensation.

Bad luck?!