I can't provide documentation for a negative. Hyundai Motor America (HMA) is not going to publish documentation that says they don't provide something (loaners). For the same reason, no one is expected or required to state, or provide proof, that they don't beat their wife and children.
But I have been on this forum since January 2009 and know what many members have been told and experienced, and have never seen any documentation from Hyundai Motor America that says they have a blanket policy of providing loaners when a car is being serviced in or out of warranty (except in certain cases that I mentioned above, at the discretion of HMA). Obviously, in some prolonged warranty repair situations, HMA has reimbursed the dealer for loaners as a matter of goodwill, sometimes to reduce the likelihood that an owner may file a Lemon Law Suit against HMA.
A fair number of dealers (which are not owned by Hyundai Motor America) will provide loaners to certain customers, depending on the repairs needed. Dealers may also make promises to customers about loaners at the time of purchase, but those are not generally reimbursed by Hyundai Motor America. HMA does not own dealers in the USA.
The fact that the 2011-2016 Hyundai Equus had concierge service similar the Genesis Motors is well known, but probably no longer documented on a Hyundai website since 2016 is no longer a current model. So I don't have any documentation on that. There is ample discussion of Equus concierge service in the Equus sections of this forum.