Your explanation is a bit odd but the results are correct.
This part you got dead on. It isn't the daisy chaining or the number of appliances connected to the strips that cause the problem but the total current being drawn though them that can cause problems if any one of the strips has its capacity exceeded. If you daisy chain three strips rated at 10A each, as long as the current passing through any one strip (including any other strips connected to it) doesn't exceed 10A, everything will be fine. Example: you have three 10A rated strips with a total load of 3A on each strip to be daisy chained together. The first strip will draw 3A, the second one that has the first strip plugged into it will draw 6A, and the third one that has the second strip plugged into it will draw 9A. It is possible to exceed the capacity of a strip but using 15A rated strips will avoid that danger when used on an outlet in a 15A circuit. Using strips that have their own breakers will also protect from overload.
In the case of the Christmas tree light example, the problem isn't from the wall socket, which is designed to handle the load, but from the plugs and adapters themselves which are rated for less than the house circuit. If using multiple strings of Christmas string lights on a single wall socket, it is far safer to plug each string into a strip that is rated for the total load.