The issue occurs when you simply move the material node itself and click the 'Apply' button to begin compiling shaders. Once it has completed, the number of texture samples increases for the Stats and Mobile Stats by a single sample.
This only occurs once and will not continue to increase the number of texture samples if you follow the steps multiple times. I tested this from 4.9.2 up to 4.12 preview 1 and the issue occurs in all versions. I did not test this on any custom materials I created, but only on the Starter Content.
Perhaps the default texture sample count is not correct, and after a re-compile it is returning the correct values?
I have added a video link to the second second URL field for further clarification on how to reproduce the issue.
1. Create a new blank project for Desktop / Console and Maximum quality, with Starter Content.
2. Open up StarterContent/Materials/M_Ceramic_Tile_Checker
3. Enable both Stats and Mobile Stats, wait for the shaders to compile.
4. Note down the results.
5. Pick the material node M_Ceramic_Tile_Checker itself, and move it to the right/left.
6. Save/Apply the changes and look at the Stats/Mobile Stats again.
Outcome The number of texture samples increases by a single sample.
Expected The number of texture samples remains constant.
Head over to the existing AnswerHub thread and let us know what's up.