take at one's word

take sb at one's word AND take sb's word for it (trust, accept without proof) — верить на слово, принимать на веру, поверить слово; поймать на слове

Example 1: You can't take anyone at their word nowadays. — В наше время никому нельзя верить на слово.

Also
take sth on faith

Example 1: Since he said he'd agree to any of my ideas, I'll take him at his word.

Example 2: He had a huge gun to my head, so I pretty much took him at his word.

Example 3: She said she wanted to help out and I took her word for it.

Example 4: I have no firm evidence that Bob's responsible for the errors — you'll just have to take it on faith.

[поверить на слово]