Can this water damage be explained by lack of gutters and grading issues?
You've really got a two-step question here

Would a lack of gutters and grading explain the water?
The simple answer is yes. That's the source here.

Even without gutters and proper grading, should the foundation walls still be water proof if they were constructed correctly?


It's that second question that will get you. Your basement walls comprise an access point for water. They're almost always concrete, which is porous and will let water wick inside. To help prevent this, you have an ecosystem to help channel water away from the basement walls. That ecosystem comprises

Gutters - Collects the water from the roof and helps to channel it away from the foundation
Sloping - Naturally moves water away from the foundation via gravity
Weeping tiles - Typically a &quot;sock&quot; covered drain pipe with holes, this collects water seeping down by the base of the foundation and helps to channel it away (think underground gutters)
Waterproofing membrane - The foundation should have some sort of waterproofing to help the water reach the weeping tiles and get channeled away
Sump pump (optional) - Sometimes the water comes up from under the foundation. If this is the case, pipes in the basement floor will channel the water to a catch basin, where a sump pump lifts the water up and out, typically combining it with gutter discharge (older setups did this into the sewer, but this could permit flooding into your home in the case of torrential rain)

You probably have #3 already (few places don't require some sort of weeper at the basement wall), but I would have someone investigate (or do it yourself and dig a hole, carefully since older weeping tiles were literally ceramic tiles). It's #4 where I see a giant red flag. You want some form of waterproof membrane to keep the water from seeping in because gutters can clog and ground can settle and/or erode so you no longer have a proper slope.
If I were you, I'd consult with an expert on the water table and drainage. You need to know if that was all rain water, or if there's seepage from the water table. I would then demand the contractor excavate the basement walls and apply a proper waterproof membrane. It will be costly, but it will be more so once the walls are finished in the basement. Don't rely on slope and gutters to do it all.
It's also worth checking to make sure your sump pump isn't discharging into the sewer. It might also be a good idea (while the basement is torn up) to add a sewage backflow preventer.
Fix this now, or you'll find your basement damp, moldy and possibly water damaged.