All the experiments used the same cell preparation, the same buffers, and the same equipment. Statistical inferences let you make conclusions about what would happen if you repeated the experiment many more times with that same cell preparation, those same buffers, and the same equipment. You probably want to extrapolate further to what would happen if someone else repeated the experiment with a different source of cells, freshly made buffer and different instruments. Statistics can't help with this further extrapolation. You can use scientific judgment and common sense to make inferences that go beyond statistics.
Statistical logic is only part of data interpretation.
It is not enough that your data are sampled from a population. The assumptions of independence is easiest to understand by studying counterexamples. You are measuring blood pressure in animals. You have five animals in each group, and measure the blood pressure three times in each animal. You do not have 15 independent measurements, because the triplicate measurements in one animal are likely to be closer to each other than to measurements from the other animals.