My son has had his motorcycle in storage and has been paying insurance on it. He has had to pay for monthly insurance as if he had been driving it. Is this right?

You used to be able to have insurance for only part of the year but no longer. (At least with the three companies I checked with.

He doesn't have to have insurance but it's a good idea to have at least coverage for theft and damage.

Most states do require insurance if the bike is registered even if your not riding it.

No, Most Insurance Companies make you take out a Year Coverage in which most people pay monthly. All the riders I know and Myself who has their bikes paid off cut the insurance once the riding season is over and the Insurance company by Law has to pay you back the difference.
If your son's bike is paid off then I would have him call the insurance company to get insurance off his bike.

for fire, and theft only if in storage

Most insurance companies will allow you to suspend all insurance but comprehensive, which covers it against theft or vandalism. I've done this myself.

If his motorcycle is in storage he doesn't have to pay insurance on it, as long as he doesn't ride it or plan to ride it.

When he DOES plan to ride it, he needs to resume coverage on the bike.

If he owes money on the bike - if he's financing it, then he absolutely has to keep insurance coverage on the bike. It's one way for the bike dealer to protect their/his investment, since, until he pays it off - they still have a lien on the bike.