No, it's still not an issue. Check out the table for 256 bit numbers in the article you linked. To get a 0.1% probability of even a single collision, you need to generate 1.5e37 hashes. At 10 TH/s, that would take 3e17 years. 10 million times longer than the age of the universe.
The birthday paradox basically says that you can expect a collision when you've explored the square root of the problem space. For birthdays, you expect a collision in a group of sqrt(365) ~= 19 people.
For a 256-bit hash, you expec a collision in a group of 2^128 hashes. That is still huge. Absent a weakness in the hash being found, it's unlikely anyone will ever generate two colliding hashes.
The chance of two hashes being equal is small but the number of two hash pairs grows exponential to the number of hashes.