I hear about sticky fish eggs but can't say I have had eggs stick to me where a little water didn't rinse them off. I know some fish do lay sticky eggs like Fatheads where they purposely stick the eggs underneath rocks or even under lily pads. I can't imagine any bird flying around with a Perch ribbon stuck to it.
If you watch video of fish farms, they often stir the milt into the eggs with a feather. If the eggs stuck to the feathers they would use a different tool.
I have an overflow culvert that runs continuously out of my pond. There are often small fish coming up the stream and in the pool below the culvert. Many fish do move up stream and in a seasonal flood they go everywhere. I believe this is the most common method fish get into new water.
Remember the fish can be very small and in a tiny stream of water and get into your pond. That event only needs to happen once and in a matter of seconds you have a new fish. Think about a good down pour of rain and how you see streams of water run across the ground where there is normally dry ground, that's all it takes.
