Thats absolutely not true in the case of Unagi. Also, "sushi" is simply a preparation technique, and if you ever said that "the whole point of it is its freshness" to a sushi chef they should bash you over the head, because that makes their job moot and its totally offensive. Anyone can catch a fish right out of the ocean and eat it.. but its the preparation and attention to detail that matters...
In the case of Unagi it`s 100% of the time always cooked and covered in tare or cured in shirayaki. You never eat it raw. You eat Horse meat sushi raw before youd ever eat raw Unagi... (yes, Horse Sashimi is totally a thing and NGL its fucking delicious)
And again, its not about the freshness, and thats not what makes sushi taste good... With most fish, if you pull it right out of the ocean and cut it and make sushi out of it, it hasnt had enough time sitting to develop the right texture and flavour to even taste good and will just be like eating chewy, flavourless gunk. You NEVER eat Tuna right out of the sea for example - it takes at least 4 days of sitting before its even remotely ready. Same goes for Salmon or even Octopus...
Freshness only truely matters for a few things - such as Uni. You cant let Uni sit or else it goes real bad real quick. Same goes for Ikura or any roe, really...