"There should be a statement in the log books that say exactly what has been repaired/replaced"
Which "log books"?
The maintenance record for an aircraft can take many forms. For a start, on a G or N you will have an airframe logbook, engine logbook, propeller logbook (if VP prop). The first two logbooks are supposed to have flights written up in them. On a Part 91 N the prop logbook has details of maintenance work only (no flight times).
Then, and here we are looking for a smashed airframe, you can have as many airframe logbooks as you like. So, the one with the details of the relevant work can simply go "missing".
Then, a lot of stuff is never in the logbooks, because the maintenance firm types up a loose sheet logbook entry. You are supposed to attach that into the relevant current logbook, but you don't have to. There is no requirement for a logbook to look like a "book" at all; a collection of loose sheets will do and in fact the records kept by maintenance firms are just that; a load of sheets in a ring binder.
Also some work, much more so on planes that are privately owned by 1 person, can be done without a logbook entry of any sort. It can be for good reasons; for example, Lycoming's QA is so atrocious now that some American buyers of new planes are sending off their engines to be taken apart and have bits properly balanced, but without any paperwork trail because since the work is not being done by Lyco's distributor chain, it would invalidate the warranty. Or work can be done without a paper trail for all sorts of other reasons.
On top of that, I know for a fact that most owners never bother to collect maintenance records together. A 30 year old plane will have been worked on by probably dozens of firms, and there is no way to find out who they were. Google might reveal some dodgy photos taken by nosey plane spotters which might enable you to ask pointed questions about witheld information, but if it's not on google it won't be found.
When you buy a used plane, it's just like buying a house. You buy what you can see and what you can inspect, and you take a chance on the rest.
The other thing is to think about why buy such an old plane.
The reason planes last as long as they do (decades) is simply because owners are forced to pour money into them. Interrupt the flow of cash and the CofA is lost, and you have a lump of metal worth its scrap value. The firm doing the annual CofA has you over a barrel; they can refuse to issue a CofA because they have discovered an extra VHF antenna which somebody fitted years ago and whose fitting was not properly writtenup, and a CAA AAN obtained for it. Your plane is now worthless until you stump up for whatever work they feel is needed.
Over many years, the amount spent on keeping it going will be much more than it was bought for.
This means that on average every penny you save on buying a plane say 30 years old, you will spend on extra maintenance over the next 15 years what you would have spent if you bought a plane say 15 years old.