The question is broad. What is the physical atmosphere? The spiritual? What is the history of each person involved? What is the covenant between the man and wife? Is it part of their custom to have another party present when dealing with members of the opposite sex?
As a matter of character, or a question of trust in the wife, the scenario begs the question "Is she a Proverbs 31 woman"?
Proverbs 31:
10 An excellent wife who can find?
She is far more precious than jewels.
11 The heart of her husband trusts in her,
and he will have no lack of gain.
12 She does him good, and not harm,
all the days of her life.
13 She seeks wool and flax,
and works with willing hands.
14 She is like the ships of the merchant;
she brings her food from afar.
15 She rises while it is yet night
and provides food for her household
and portions for her maidens.
16 She considers a field and buys it;
with the fruit of her hands she plants a vineyard.
17 She dresses herself with strength
and makes her arms strong.
18 She perceives that her merchandise is profitable.
Her lamp does not go out at night.
19 She puts her hands to the distaff,
and her hands hold the spindle.
20 She opens her hand to the poor
and reaches out her hands to the needy.
21 She is not afraid of snow for her household,
for all her household are clothed in scarlet.
22 She makes bed coverings for herself;
her clothing is fine linen and purple.
23 Her husband is known in the gates
when he sits among the elders of the land.
24 She makes linen garments and sells them;
she delivers sashes to the merchant.
25 Strength and dignity are her clothing,
and she laughs at the time to come.
26 She opens her mouth with wisdom,
and the teaching of kindness is on her tongue.
27 She looks well to the ways of her household
and does not eat the bread of idleness.
28 Her children rise up and call her blessed;
her husband also, and he praises her:
29 “Many women have done excellently,
but you surpass them all.”
30 Charm is deceitful, and beauty is vain,
but a woman who fears the Lord is to be praised.
31 Give her of the fruit of her hands,
and let her works praise her in the gates.
Note these again in particular consideration of the question:
11 The heart of her husband trusts in her,
and he will have no lack of gain.
12 She does him good, and not harm,
all the days of her life.
23 Her husband is known in the gates
when he sits among the elders of the land.
25 Strength and dignity are her clothing,
and she laughs at the time to come.
If my heart trusts my wife, it is not afraid of her actions. If all the days we have been in covenant she has brought me no harm but much good,I have further foundation for trust. If in her dealings she makes my name known, she removes any potential for a man to excuse improper conduct. Thus, I am further empowered by my wife to act on her behalf if needed. In doing these things she is submitted to the Father and to me as her Husband. Thus, she is under a covering. My wife will not be swayed by any man because she is covered by strength and dignity.
As men, we are priests and protectors of our family. Our part should start long before the hypothetical presented in this thread. Righteous answers are as numerable as the potential specifics to the hypothetical. Are there times and situations where it is appropriate, certainly. Inappropriate? Certainly. Where a wife should be able to call on her husband for help? Certainly. Where a husband should intervene? Certainly.
I offer a slightly more specific situation. If it were my daughter the man was talking to, should I intervene? My wife was entrusted to me by her father. She came from his covering and household to mine. Her provision, protection, covering will not decrease. She is the daughter of our Creator. Treat her as such. You may answer to me otherwise, and possibly, to Him.
That verse quoted by C4L would apply, perhaps.