Am I right that too strong a radio signal (from too long a wire) can
hurt the radio?


Depends on the radio. The input gain device may be adversely
affected by too strong a signal. Being driven into saturation can
result in failure of some devices. This was a problem with some Sony
radios. It was a problem on a few inexpensive radios. It was a
problem on a number of early solidstate radios.

Today, receivers have overload protection before the first active
device. Sony installed diodes before the front end of their affected
devices. And most input devices used today have sufficient headroom
in circuit to prevent front end overload in all but the most extreme
cases. Buffers, and IF amps will more quickly overload than many
front ends, today.

But if you're talking about SW, unless you're near Antigua, or
living in Western Europe, you're not likely to encounter signals
strong enough to cause overload problems. A few domestic SW players,
if you're close enough. But not nearly what it used to be.

So, depending on your location, your concern may be a non-issue.

That said, it's something that's worth bearing in mind.