First thing to point out here is that the talk isn't about the Marksmen champion archetype being weak. Corki is out of control mid-lane and has been for a while now. It's about the Farmer lane position being weak.
The general consensus among high Elo players right now is that, as a class, the Farmer role is weak due to the level of pressure on bottom lane and the higher XP that Junglers get. The higher pressure means bottom lane champs need to back earlier to avoid getting killed, averaging 800ish gold available for purchase. Since they typically can't afford a BF sword on their first return, it leaves them at a hefty disadvantage since they're sitting on a pile of gold waiting to be useful until their second back, barring the bottom-lane clown fiesta going drastically in their favor rather than just wasting Summoners (keep in mind, death count in high Elo games tends to be much lower).
The higher Jungler XP means that the Farmer and the Support are the only champions not getting solo XP. Being at least one to two levels behind everyone else is a pretty significant disadvantage that takes a pretty major gold investment to overcome which is, again, difficult to safely acquire due to aforementioned bottom lane clown fiesta.
Even if bottom lane Mages or Bruisers or whatever became a popular pick bottom lane rather than Marksmen they would still be weak in the Farmer role because of the exact same reasons mentioned above (high pressure and level disadvantage vs everyone). However, they would at least have the advantage of being able to pick up a Longsword or a Amp Tome on their first back.