It depends. If the wall anchors are, say, 5 years old, and you don't have any further signs of the original problem continuing, then it may be fine. However, if they're new, you would be less sure it the anchors are all that need to be done.
Usually, the anchors are installed to combat hydrostatic pressure. If the pressure is sufficient or if the install isn't 'sound', then the problem could persist. That's why its 'age' is important to me.
At the same time, if you like the house enough, ask to see the installation paperwork from the seller. Take it to a Structural Engineer for evaluation. Spending a few hundred $$$ for 1) a home you really like, and 2) for a home that will most likely cost you a few hundred thousand $$$, is money well-spent for peace-of-mind. If the job was done by the homeowner, themselves, I'd be a bit weary unless you had it professionally evaluated.
You will have an ASHI-Approved Home Inspector, eh? And you also have a Real Estate Attorney, right? These are people who look after YOUR interests. Again, for the same reasons above, the $$$ you spend on this is money well-spent. IF there's a problem down the road, the Attorney is already 'in your pocket'. The costs for both are usually between $250 and $700 for an Attorney, and $250-$400 for an ASHI Home Inspector. My best to ya and hope this helps.
PS: No one from 'here' can tell if the home is structurally-sound. As for how long they last, I've seen them STILL working for 15 years+. Here's a link with some info. (THe info is all over the WEB if you search for wall anchor.) Wall Anchors from Matthews Wall Anchor Service.
PPS: I'm not an Attorney, Home Inspector, or a Wall Anchor Contractor ...