A stretch as far as you describe seems a bit excessive

Maybe it was just what he had?

Auto parts stores often have something known generically as a
"recovery strap." Usually it's a flat woven belt but some light duty
ones are braided round ropes, like a water ski tow rope for Paul
Bunyan. I wouldn't think that a bungee, capable of ~ 3x stretch,
would be my first choice. Definitely they have some "give" for just
the reasons you mentioned, though, and also so that spring action can
give you a little more oomph. (Presumably to pull the stuck vehicle
forward, not to pull the tow vehicle back!) Some websites seem to
indicate that 20% stretch is about it.

Here are some examples and instructions:
http://www.keepercorp.com/prod/vrs1.htm
See also, for instance, http://asa4wdc.org/content/safety/recovery.html

How does that old saying go -- four-wheel-drive lets you get a lot
further from help before you get stuck?

--Joe