I have never heard this before.
Actually we would not even think of attending a different parish. There was no smorgasbord when I was growing up. No need to pick and choose, but we now live in a different world. If you were travelling or away you went to the nearest. There were no differences parish to parish apart from the sermonabilty of the pastor. You were safe wherever you went.
I have also never heard of a prohibition, and I'm a cradle trad. There was an expectation -- most of it logical -- that you would attend the parish closest to you. But doctrinally orthodox parishes were everywhere; none preached heresy or said "a new Mass." I would say you were expected to accept the local parish God gave you in submission to His Providence and to counteract any spirit of willfulness, but the only cross suffered was the particular personality of the priest and his teaching style. As now, some priests were unhappy, other priests were boring, and others were inspiring, but ALL of them were faithful and could be counted on to tell the Catholic truth straight-up.
Families with lots of young children sometimes have trouble getting it together to get to a particular church on time for that Mass -- hence the convenience of so many options within 5-15 minutes' driving distance. So that was the reason we sometimes didn't go to our most local parish, one mile away.