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Shemos 19:23
ויאמר משה אל יהוה לא יוכל העם לעלת אל הר סיני כי אתה העדתה בנו לאמר הגבל את ההר וקדשתו
Moshe said "the nation can't come up, because you warned us to set boundaries around the mountain"
It's true that Hashem told Moshe to set boundaries (verse 12), but when did Moshe actually set the boundaries, or warn the people? It isn't anywhere in the intervening verses.
Possibly related: What was the boundary set around at Har Sinai?
Without access to commentaries at the moment, we can infer something from the 2nd verse after the one you mentioned, that says that Moshe went down from the mountain and said to them... meaning that he said to them about the warning not to go to Mt. Sinai. "said to them" can't mean the words of the 10 commandments, because the commandments are introduced by "G-d said all these things..". We also see elsewhere (paragraph following 10 commanments for example) that only after they heard God's voice directly, they got scared. So, I infer Moshe warned just prior to God speaking.
Note that this does not contradict Moshe's answer to God, as mentioned in the verse you listed. All Moshe says is a fact; He didn't say, "I told them not to do it."
Another possibile explanation is when Moshe says in verse 15, Moshe says, "prepare yourself for the 3rd day." Although he does not state HOW to prepare, it's possible that within this preparation Moshe may have explained the "border" rules, even though the Torah does not explicitly say so.
Lastly, at the end, the border did not matter, because everyone was so scared that they backed away from Mt. Sinai, anyway.
