I think it'd be fair for donors to get a tax break according to how much the stock is worth when it's given to charity.
An admittedly brief review of the news articles about this event seem to contradict that. The author of this article interpreted the drop that way in order to better make their case, because...well...they have no case.
Below I have listed a few articles from the front page of Google results for this subject. Not a single article that I could find mentions investor worries that the donation was driven by the CEO's lack of confidence in the company. Rather, investors were upset because JP Morgan allowed these shares to be released from a lockup agreement with virtually no advance notice to shareholders. They were worried that the shares could potentially be sold by the charity almost immediately, which would have flooded the market with insider shares far earlier than investors expected.
https://www.inc.com/associated-press/gopro-shares-fall-as-ce...
https://money.cnn.com/2014/10/02/investing/gopro-charity-sha...
http://fortune.com/2014/10/02/gopro-shares-woodman-charity-l...
https://www.wsj.com/articles/gopro-ceos-foundation-doesnt-in...
In the most common scenario, that would mean people could receive deductions on a larger tax basis than the value they actually donated. If they waited long enough, they could even receive a tax break that was greater than 100% of the amount they donated.
Sure, but the reverse is true as well - the contribution could increase in value, which benefits the charity. And if that happens, he doesn't get to claim the difference as a deduction.
Furthermore, he gets the tax deduction based on $500 million because that's the amount he's giving up at the moment he makes the (irrevocable) decision to divert the funds to charity. (The alternative is for him to liquidate and hold onto the $500 million himself; he's getting a tax deduction for not doing that).