So the conversation reminds me of a film I got when Netflix was still DVD rentals only.
The Vanishing (1988) which is a Dutch suspense film. Very good film and I highly recommend it.
I looked it up on Netflix Streaming, though, and there is another:
The Vanishing (1993) starring Kiefer Sutherland, Jeff Bridges, etc. Apparently a remake of the Dutch version, but not as good according to IMDB. I haven't seen it yet, so I cannot really weigh in on how it compares.