No.
But it refers to the fact that if the level of trust between two people is so low that the words "I promise" have to come into play, that such will probably be broken later.
After all, if someone is truly trustworthy, their word alone is sufficient, and no "I promise" or "I cross my heart" or any other oath is needful.
Finally, if someone has told you this, you should not bank on any future statement or promise of their's.
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