I disagree with that. Even from a basic half-guard, and even with my back flattened to the mat, I hit plenty of sweeps from wrapping an overhook, other hand on their hip, disrupting their base by moving their trapped leg across the mat, and sorta shrimping/rolling towards the side with the overhook.
I'd say that's just as valid as the underhook, and I feel just as likely to get my guard passed with either.
Sure, you can hit a few legit moves from bad positions, but that doesn't make those bad positions 'just as valid' as more advantageous positions. The point is that your opponent has much more control over you when your back is flat on the mat and he has the underhook, and more importantly, his array of options is far greater than yours. This is the reason why people prefer to pull certain half guards (i.e. on side with underhook, foot on hip, deep half, half butterfly, inverted half) while eschewing others (i.e. underhooked and cross-faced, opponent has back turned, reverse half guard, etc.): The former variants offer lots of offensive options for the bottom player, whereas the latter offer very few.
Now, if you feel just as likely to get passed whether you have an underhook or an overhook when playing a 'basic' half guard, I'm curious as to the level of your sparring partners.