If you're a fan of Mythbusters on The Discovery Channel, you'll know just how hard it is to erase the encoding on magnetic strips. They were investigating the old legend that wallets made from electric eels will demagnitize the strips on credit cards. They, not surprisingly, found that they could not reproduce this legend in their shops using eletric eel skin. It was busted.
If you watch the show, you'll know that they ususally don't stop with showing that a legend is a myth... they will take it to the next level and try to see what it would actually take to make the outcome in the legend happen. So, they tried to figure out ways to erase the encoding on plastic cards. They tried rubbing two cards together strip-to-strip, exposing them to toy magnets, etc. In every case the tests failed to erase the cards. The only thing that they found that would wipe the cards were they powerful "degaussing" magnets (AC powered) that are made to erase magnetic tape and computer floppies.
At this point I'd consider it a CM legend that cell phones can de-mag the cards. If toy magnets don't do the job, I can't see how a weak RF signal from a cell phone could. I'd would suspect that it's anocodotal since people often carry cells in the same places as their park tickets, so people assume it the phones. As for spare batteries, there's no magnetic field around a battery that's not in use.
It's true that the mag strips on card do occasionally go "bad" (we had an AP go south once), but the Mythbuster guys showed that it's pretty hard to make it happen from an external source.