Sterizers only collect the parasite when it's swimming and looking for a host.
This only happens for about 48 hrs.Once the parasite finds a host the sterizer is useless.The chance of you getting ALL the ich parasites through the sterizer before they find a host is very slim.
It takes only one parasite and you'll have hundreds of parasites, called tomites.It's like spraying a few bees with Raid and claiming the hive is dead.
But there is hope for those that choose to live with Ich.It's said that they only reproduce around 56 cycles before dying off.That's about a year,so if the fish stay healthy it's possible to be Ich free.