Well it is a bit of a supposition but everything we've seen so far of the fairies is if they had Direct help from one of the Courts they would have just broken into this place and stolen whatever the fuck they wanted without getting caught. By that point in history this particular religion is almost non-existent if they had the backing you're saying to get artifacts of Resurrection that means favors to the point of getting the armies of Summer to March or very least a large contingent of Summer and if they had that this place stood no chance. We know just the three of them were very close to breaking out on their own before David intervened if they had actual backing from the summer court it's a wrap.
There's also the fact in myth so this is with a massive grain of salt only three of the round actually had big inroads with the fairies that was Gawain, Lancelot and Arthur who in order was given a blessing of the Sun at some point in his life by fairies Lancelot was raised and possibly bourn by the Lady of the Lake and Arthur was granted his sword by the Lady of the Lake. None of the other members of the round had any particular connections to fairies outside of slaying trolls and other types of Supernaturals so it's questionable if they would have a relationship outside of being sworn to someone who has a connection.
Also the summer fairies gave an alternative they said they could not resurrect Arthur so we will put him on Ice if they could resurrect him they would have done so already because that's what he asked for to start with.
