What's wrong with the advice:
-Removing horizontal lines decreases readability in the complex examples given
-Vertical lines are very helpful when there are more than three columns
-Serifs have actually been found to be more readable due to their distinct letterforms and can be comprehended more quickly. San-serif fonts are fine too though. Basically, choose a font that has good legibility.
-Don't rely on light gray lines, because they might not be visible on all screens, or in various environments, and likely won't translate to print
-Double horizontal lines for column headers are fine.
-Overall, if you're presenting important information, usability is much more important than minor aesthetics.
Here are some more actual tips for laying out tables:
-Ensure that if a horizontal line needs to be scannable, that it actually has enough padding, or a horizontal separator, be it a dotted line or some other type of visible anchor
-If columns have a lot of information, a table may not be sufficient. Consider aggregating individual rows into a card format.
-Padding is your friend. Also, be consistent with it. A table with too little, but consistent padding looks better than one with more breathing room and inconsistent padding.
-Most information should be aligned left. One exception is currency. That should be aligned right