Like you, my kitchen is spotless and we leave no food out at all. Also like you, we get the occassional ants. There are two reasons why you might find them in your sink, in my humble estimation:
1. You have a garbarator enroute from your sink to your drain, as we do.
2. You leave any kind of dish towels or dish rags out (which have trapped food, sugars, oils).
The garbage disposal is a great place for grease and particulate buildup. The only environmental way I have found to clean it (other than the cooling and water waste aspect) is the grind about 8 cups of ice cubes and 1/2 a lemon down my disposal each week. Also, don't leave any used dish cloths or towels out at all.
In hot climetes, like ours, I have found ants sneaking out of electrical sockets. Rather than using a lot of harmful poison sprays you can use white vinigar, household cleaning ammonia, or a "windex" like product and just wipe the face plate and wall around the sockets and switches. Don't use too much, IE: not to drip water base products inside your electrical outlets....just a light spray on a cloth and wipe around them.
At my place, it seems to prevent any ants coming out for up to 4 weeks before I need to wipe them again.
Hope this helps.
Personal ant prevention experience :)