Are UV LEDs really dangerous?
The limits of "safe" emitted light are very complicated. You can read about the basics here.

A rule of thumb I have heard is if the emitted power is over 5mW, protection should be used. Since the LEDs you linked are capable of 10mW, yes they can be harmful. Do not use them until you understand how they can be harmful and how to prevent it. 

UV is particularly dangerous because we can't see it so our blink reflex won't help. To safely work with these LEDs you should get a pair of glasses that block the possible wavelengths the LED can emit, 390 to 405nm ±2.5nm. Examples here.

This paragraph answers an edited out question in the OP wondering why he had a UV pen with no warnings. As for your UV pen light question, it is likely the power was low enough that it was not harmful. Less than 0.39mW (roughly) is considered eye safe so under that no warning would've been required.