Oddly, he finds that far too authentic to be real. Since he's had to go back and re-examine all his interactions with the Natasha of his world, he's distrustful of anything that looked that genuine. She was a master at making them see exactly what she wanted and it would have been a measure of stiltedness that would have might have convinced him it wasn't fake.

"It's been years, if I'm not over it now I'll never be. Thank you for the offer."

However even if he's unconvinced that her reaction's are genuine, he doesn't suspect she has anything like the ulterior motives of what he considers the original. He finds it more likely that it's just something she does to cultivate relationships for good or bad.