Buttinvader

Former AASP for Micro Center here, I can confirm this is exactly how it works as an Apple Tech. Apple's system for repair is super difficult to work with, and they do require you complete certain course work before ordering parts for newer computers. It also doesn't help that this system is incredibly hard to navigate (as of last time I worked with it 2 years ago) and it's not guaranteed that the system with the training's will talk to the system with that allows you to order parts. 
 
My guess is in line with Diglio's, there's most likely some issue systems, training, or otherwise than the part not being physically available. The other thing is that the Apple Store most likely doesn't have a designated "Parts Coordinator" If the repair shop is big enough, they'll have a full time person in that position, those people are usually the best at getting you through stupid stuff like this. My suggestion, just find larger chain retailer that's Apple Certified and has a sizable repair shop. They usually have those resources. 
 
p.s. My favorite part with IMac screens,was when they're shattered like Ltt's is, you're instructed to cover the entire surface in painters tape to prevent it from completely disintegrating. 

I am part of an AASP company, and certified in all Apple Devices for repairs, and I want to start by saying that it is quite a nightmare to go through Repairs and get parts needed for repairs. 
 
To start, just going through the process to get parts ordered takes forever. It doesn't matter if you know for certain which part is needed, you have to go through their troubleshooting guides which are both a nightmare in their wording, and send you in circles when it comes to testing. 
 
Second, I have done a repair for the iMac pro recently (within the past 3 weeks) and was able to get a Logic Board, Screen and Power Supply without issue. Granted I am in NYC so it is possible they had a supplier close by. The repair process was a pain (as are most Apple Repairs) and the turn around time you have to do the repair is only 10 days. That means from the moment you receive the part, you have 10 days to install it, serialize it in the system and send the old part back for shipping. 10 days doesn't seem like a short amount of time, but when the part you ordered requires other parts that are broken to test, 10 days flies by. 
 
Third, in my 5 years of doing Apple Repairs, I have never had them turn around and tell me they weren't able to receive the part and thus the repair would be decline. What most likely happened, and what I have seen in the past, is that the store had no certified employees for iMac Pro repairs, so none of them were able to order the needed parts. If that isn't the case, then you were straight up lied to. From the day the product is available for shipping, items are available for order (I have had this happen on multiple ocassions, including the day 1 release of the Mac Pro Trash Can video card recall). 
 
Lastly, the parts you need to replace are a complete pain. With Apple's new Security in-place, and with High Sierra, getting everything to function properly blows. There are issues with screen brightness, drives not running at proper speeds, etc.. I wouldn't be surprised if you do get this thing repaired, that you won't have issues at a later date. 
 
Hopefully you guys can find an AASP within a short drive of you to have the part(s) ordered and repaired. Granted, the repair cost for a screen, logic board and PSU are going to be pretty insane.