On the modules branch I ended up changing the beginning of Prcoess::openDocument from:
#if JUCE_IOS
return [[UIApplication sharedApplication] openURL: [NSURL fileURLWithPath: juceStringToNS (fileName)]];
#else
To:
#if JUCE_IOS
return [[UIApplication sharedApplication] openURL: [NSURL URLWithString: juceStringToNS (fileName)]];
#else
With the later, HyperlinkButton starts working as expected on iOS.