Hairpin telomeres cannot be replicated with normal DNA synthases, they need a special enzyme, telomere resolvase (source), to replicate and appropriately fold them.
I read your source and I think there are a few salient points to note.
Firstly telomere resolvase' is, like 'telomerase' a descriptive title for whatever protein is actually performing the telomere resolution. Among the proteins they identify as capable of this is a topoisomerase, hadly an unknown. Similarly the specific
E. coli phage TelN resolvase they identify is said to
function through a reaction mechanism similar to that of Type IB topoisomerases and tyrosine recombinases
and has structural similarity to the integrase/ tyrosine recombinase proteins.
Other proteins clearly exist which can resolve the cruciform Holliday junctions.
The embo J. paper you go on to discuss may well be talking about a totally different 'telomere resolvase' it need not be the same as in the source paper, a similar possible confusion as to that between human and yeast telomerase.
While the paper says that the resolvase is a site-specific recombinase rather than a general Holliday junction resolvase it is surely relevant to note that a general Holliday junction resolvase might well preform the samme basic function and be a very suitable substrate for a site specific enzyme to evolve from.
TTFN,
WK