7.0 Photoshop cannot read layers on newer Photoshop

Setting layer visibility off does not delete the layers. They are still in the Document. If an old version of Photoshop can not support a layer that layer's visibility can not be set  off or on it can not be processed.  With max compatibility there is a full size composite layers saved in the layered file that an old version of photoshop may be able to use for the image.   Does  the old Photoshop versions offer your client any options for the layers it can not process like a substitute layer. or delete layer. There are new layer kinds, Layer styles can have more effects.  Layer kind may have option and attachments not available in old  Photoshop.  Maximum compatibility does not eliminate compatibility problem.   Like Lightroom the old Photoshop version can use the Composite in the document instead of layers.   Maximum compatibility includes a full size composite for your documents image so old versions of Photoshop can render your image even when there may be layer that photoshop can not process.

Wow, Photoshop 7 was released in 2002, so that's pretty far back for backward compatibility--and Photoshop is doing a great job with the file. From the screenshots, it looks like the issue is that the nested layer groups aren't showing up. Hierarchical layer groups weren't released until Photoshop 8. When you know you're trying to make a file as backward compatible as possible, try to avoid features that weren't available in the targeted version. Also, according to this article from ProDesignTools, you could try saving a .tif.