It's a cryptographic hash function, but not one suitable for all of the same applications as SHA2. It has security characteristics that other hash-table hashes (for instance) lack.
If you know the key, it is as weak as it gets (as the paper notes too, you can construct collisions easily if the key is known), so I disagree.
Honestly, I really don't care about this debate, except to the extent that it's about whether SipHash "isn't cryptographic and therefore you might as well use CityHash or SeaHash", which just isn't true.
I agree. SipHash is certainly strong if you don't know the key.