I mean, its almost certain that it wouldn't be perfect at first. Hell, it would probably take several seasons to come close to getting it right.
However, when range has actual trade-offs, and melees have actual advantages, rather than just having better or worse kits simply due to being either ranged/melee, you'll notice something being ranged isn't nearly as big of a deal.
It wouldn't be like now when range is simply better than melee, so there wouldn't be an issue with range now packing as much punch as melee. Melee would have just as much over range as range has over melee.
Another thing would be that marksmen with dashes would likely have significantly lower MS than ones without. Cases like those would likely be where the 25% differences set in. Immobile melee vs mobile ADC. Think Singed vs Lucian/Ez. The mobile carries would be the ones that would feel weakness in that regard, not so much the immobile carries who are already a risk simply because they have no mobility/MS steroid, like Varus/Ashe.
As a result, you'd also see a surge of 'wardens' as peelers, rather than just engage/disengage. Fights would be a lot more involved overall, similar to previous seasons. Fairly certain Taric would get nerfed as a result, however.
Its very likely that damage would have to be toned down a little across the board as a result of everything. With the state of damage in the game right now, that higher MS would cause many melees to simply overrun ranged. That's a very real problem in the game as well atm, and it would have to be solved in order to ever implement changes like what I've been talking about.
Now, as for which argument is right or wrong...neither.
One stems from Riot's current balance philosophy (which is clearly broken in many aspects). Its their game, so it can't really be 'wrong' as long as they're trying to refine it.
One stems from a direction they could take to make it easier to balance, and would even open them up to more diverse and satisfying characters in the future. Obviously they don't have to use this approach, so it cannot be intrinsically 'right'.
Balance is entirely dependent on numbers/fact; its pretty objective overall. Balance direction/philosophy is based on opinions formed around facts, thus neither argument is right/wrong because they are just balance directions, and which one is considered valid is based on which version of the game the arguments are even implemented in.