I don't understand why they say that reference counting is "slow". Slow compared to what? Atomic increments/decrements to integers are one of the fastest operations you can do on modern x86 and ARM hardware, and except in pathological cases will pretty much always be faster than pointer chasing done in a traditional mark and sweep VMs.
This isn't to say reference counting is without problems (there are plenty of them, inability to collect cyclical references being the most well known), but I don't normally think of it as a slow technique, particularly on modern CPUs.
Atomic reference counting per se is fairly slow compared to other simple operations [1]. But the biggest issue with reference counting is that it doesn't scale well in multithreaded programs: even pure readers have to write to shared memory locations. Also acquiring a new reference from a shared atomic pointer is complex and need something like hazard pointers or a lock.
[1] an atomic inc on x86 is typically ~30 clock cycles, doesn't really pipeline well and will stall at the very least other load operations.
This isn't to say reference counting is without problems (there are plenty of them, inability to collect cyclical references being the most well known), but I don't normally think of it as a slow technique, particularly on modern CPUs.