Can you do a PhD solely on repeating experiments of others?

I would say it depends:

a) If in medicine, you are the first one to replicate an effect in an independent study, then you actually did something original, namely confirming the effect

b) If in physics, you refine an experimental design to verify an uncertain outcome, or clean up a measurement to exclude artifacts, and make the effect more clear, it is also something original

The rest is in the shades of what passed in the journals as "original". But I guess as long as the experiment was set up freshly (i.e. not in the same group) and had any small improvement/change (analysis method, amount of data, statistical uncertainty, control experiments) over the original it would pass in many universities for a PhD (and I will not give my personal opinion on the level or originality required for a PhD in an average university here).

It is the knowledge created from research that must be original and not necessarily the research topic itself. May topics of research have been revisited throughout time when advancements in technology or methods allow a greater insight into the original hypothesis and results. If your hypothesis differed from that of the original research project - such as quantifying the impact of previously unaccounted variables or applying the original knowledge to a novel application - then there is grounds for originality.

I know of a colleagues research that has been based on the results of a previous researchers contribution to knowledge. When trying to apply this knowledge to an application my colleague found certain elements from the previous research did not repeat in the manner they should. This discovery highlights the original research as non-repeatable and possibly even discredits it. These results are valid and important to the advancement of knowledge.