When I come across a horrible mismatch, such as this, I ignore the apparent incorrect color and use a value which more closely resembles the color from the correct color breakout.
So Yes. I change the HEX when I see this happening.
If at all possible I do check things like the client's web presence or any marketing materials to confirm I don't see the apparent incorrect color anywhere. I also mention this to the client 1) so they can be aware there's a possible error in their brand guideline or... 2) on the wildly, off-chance, they really do want that apparent incorrect color.
Hex colors are RGB color. Some don't realize that.
Converting between color models is rarely 100% accurate and can often take visual adjustment.
On my system, using your CMYK values (56/4/100/0) results in a HEX of #81b948. Which appears very similar, but nowhere close to #70F500. Note that #81b948 is a direct result of my color profiles. That exact hex value may not be the same on any other system where the auto-conversion is concerned.
I've OFTEN seen poor color conversions in branding guidelines similar to this. It's not impossible that someone, creating the guidelines, mistyped a value. Or merely used an auto-conversion value which they never actually checked. This also can often happen if one starts with a Pantone color.. then auto-converts spot to CMYK, then spot to RGB.. again without ever actually checking the color appearance. Spot auto-conversions tend to result in more mismatches in my experience.