Maybe yes or no but when I borrowed my dads car 62 plymouth I was rear ended by a lancer. The lancer was crunched in the front and smoking and the rear of the plymouth bumper just moved about 2 inches.
This is due to differences in the understanding of collisions. Older cars were built so that the overall structure would withstand low-impact direct head-on/read-end collisions, and were relatively rigid.
The problem with making the front and rear very rigid is two fold:
1. It does not absorb any collision energy.
2. It directs energy into the passenger cell.
The result is that in a higher-impact collision, the passenger cell collapses. Additionally, much higher forces get transmitted into the passenger cell and the passengers, potentially causing more injury.
In modern cars, the front/rear ends are specifically engineered to crumple. This is why cars can sustain severe damage from low-energy collisions, while older cars may survive them. The differences are the forces on the actual passengers. 2 rigid cars colliding, even at relatively low speeds, can put very severe forces on the passengers, causing whiplash, or other internal injuries.
By contrast, in modern cars, the passenger cell is highly reinforced, including side impact protection - which was completely absent from pre 1980s cars. A side-impact, even of relatively low speed, would result in severe intrusion into the passenger compartment.