First off, you did one of the best things a prospective homeowner could do - Visit the home after a heavy rain. THAT will tell you more than Seller Discloser (which is a good thing, on paper.)
The good news is you saw no water after a heavy rain. However, relatively speaking, if the rain you had was 'light' by comparison to 'normal rain storms', you may find water when you don't want it. (JUst keep that in mind.) Also, take a look at the gutter, downspouts, and downspout extensions, and grading all around the foundation. The water may not be, directly, from the rain. If the gutters are not angled properly or hung improperly or leaking, THAT may 'fix' your problem. If the downspouts are clogged, clearing them MAY fix your problem. If the water from the downspouts runs BACK towards the house, then you need to re-grade and EXTEND your downspouts at least 3' from the foundation. At worst, re-grading all around the house to a 'level' of AT LEAST 1/4" per foot may fix your problem.
If you can read between the lines here, the answer MAY lie with getting the water AWAY from the foundation, and getting it OUT of there as well. Improper grading is the most common 'cause' of water in the basement. Have the inspector thoroughly check the 'level' and 'installation' of the gutters. Also, have him pay VERY CLOSE attention to the grading ALL around the house. (You have to realize that water travels in the path of least resistance. It can 'enter' the ground at one point, travel along a wall, and enter at a point completely UNRELATED to where the water first entered the ground.) Also, ask the inspector to give an Estimate for Repair. This is NOT a conflict of interest unless he offers to do the work himself OR he recommends someone. Try and find yourself your OWN inspector; not one recommended by the Agent (unless you have a Buyer's Agent.) Get an ASHI-Approved Home Inspector. They have to 'abide' by certain ethics. ALSO, ask about the professional background of the Inspector. You DON'T want someone who use to sell cars for a living inspecting your home! Nor do you want a 'friend' to be your Inspector (unless you're willing to lose him/her. It's OK to have this type of 'friend' look over the house BEFORE the Inspector does but I wouldn't ask them to BE the Inspector.)
As for repairing the crack, yes, you would have to dig it out and fill it with an expanding cement. (See this post: Cracked Foundation for info.) Ask the Inspector to estimate the fix for the crack too. Ask what woudl be involved too. (An ASHI Inspector is suppose to give you the Report AT THE HOUSE when he's finished inspecting so you can review it and ask questions when he's there. If the ISN'T doing this, ask WHY. You don't what to get your report many days later where he can, conceivably, 'forget' about your particular inspection.) Check out the ASHI WEB Site for 'how they do an inspection'.
My best to ya and hope this helps.
PS: I am not a Home Inspector, nor do I work for one, nor am I compensated in ANY way by ASHI. (I'm just here to help. Home Inspections and retaining a Real Estate Lawyer 'during this process' are INVALUABLE and a 'big deal' to me.)