The only way you will see stars down the bottom of a well is if someone throws something heavy down the well onto your head. I can almost guarantee you will see stars then.
Seriously, though. There are stars that can be observed during day light hours. Surveyors before the advent of GPS systems (I did this for employment in the Army as a cartographic technician) used stars during the day to work out the position of survey points and also to get longitude and latitude from a position. Most often we would use the Sun and do sun obs for the most accurate timings and positioning. This was mainly to establish survey marks for horizontal and vertical control in mapping. You can only use the brighter stars but they can be seen through a theodolite and once you have sighted the stars you will see them naked eye as well. However, the myth that the sky goes dark down a well is simply that. Sunlight is scattered in the atmosphere and that light cannot be negated by being down a deep well or hole.