Absolutely, this is correct, if your opponent pushes to a shot you don't like you can re roll out to a another shot, then you're both on "one foul" (then and only then is it like "one foul").
Then if the next shooter commits ANY foul it's BALL IN HAND, (like "one foul" at that point).
Back in the 80s this in the ONLY way we played and it was extremely strategic....again, when this game is played correctly it consistently requires more difficult shots than one pocket because you are defending ONE ball against SIX pockets all the time.....so it requires a player to be completely well rounded in banking, cutting, long shots, shots off the end rail, safeties, "two way shots", etc.
This Game is the Teacher