You know, a number of the hostels in Madrid seem to call themselves "Hotel" from time to time too so maybe this is the same case. I just checked
HotelSearch.com and there they are listed as HOTEL Rey Don Jaime I, on Calle Jaime I, 11 and their phone number is 93-310-6208.
Still, while not likely, it IS conceivable that they have BOTH a hostel AND a hotel in the same building. I've seen this setup before, but not sure if it's like this in this case.
Good luck! Saludos, MadridMan
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