Should a PhD thesis reflect the state of research at the time of writing?
Some options:

Explanatory footnotes often work well and can be used to 'talk across time' so to speak;
Appendices can also be used for covering material that may be out of sink, if you think you need to go into more detail;
An afterword can also be an appropriate way of accounting for developments between the time of writing and the time of publication. This is fairly common practice.

Basically most examiners will view the dissertation as YOUR journey through the research, rather than as an exact snapshot of the state of play in your area.
HOWEVER - they will be looking for (and be impressed by) you demonstrating that you know what good practice looks like in your field of research, and this extends to how you handle (and acknowledge) circumstances of this kind.