Dic: take someone at their word

■ to assume that someone means, or will do, what he or she says.

• when he told her to go, she took him at his word and left.

■ To be convinced of another's sincerity and act in accord with his or her statement.

• We had to take them at their word that the job would be done on time.

■ to do something as a result of what someone has said, even though they may not have meant exactly what they said.

CF.

■ my/his/your etc word: a sincere promise to do something, or a promise that what you say is true.

• I trust him to keep his word.
• I give you my word (=I promise) that it won't happen again.
• We only have his word for it that he has already paid.
• Delors claimed that Johnson had gone back on his word (=not done what he had promised to do).
• The business is doing very well. You can take my word for it (=accept that what I say is true).
• I never know whether to take him at his word (=believe what he says).
• His word is his bond (=he always does what he promises to do) .

.... Collins, WordNet, Macmillan, LDOCE