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Minimum specs does not mean it won't run on a HD, it just means you will have a miserable time as your performance won't run to the level where the devs consider the game enjoyable. This specific borderline will vary from developer to developer, as an example ubisoft for example, minimum requirements are for playing the game at 10fps it seems as you need way higher then they require.
HD vs SSD only changes load times, I done research and I not seen a single example where a game would hard not work because it was on a HD over an ssd. Albeit being on a ssd will improve performance from 30-100% load times on games.
You are absolutely right, it will run...initially!
The problem is going to start to occur when you get to the higher traffic areas and specifically Baldur's Gate the City. Then the performance is going to go right into the toilet if you don't have an SSD or a LOT of RAM - like 64GB to 128GB.
And then you will likely be looking at crashes, de-syncs, and possible rubber banding. God forbid you try to play multiplayer like that.
I think they said get an SSD because that's going to be easier and less expensive than trying to boost your RAM to 64 GB - also that would look crazy.
