I went up against this in silver. It's only strong if your team is a pile of garbage and refuses to exploit the fact you KNOW one lane is going to be 1v2 all game (barring counter-ganks). So you recognize this potential, ward against level 2 or 3 cheese gank, and then pick a durable champ with sustain and some nice burst. You abuse the crap out of enemy support until twitch gets his buffs and starts camping your lane. If they're unprepared... you can snag an early kill or force them to base and tp. If you feel uncomfortable with this risky play or can't get vision to track twitch's first clear, just let them push you to tower.
Communicate to your jg RIGHT AWAY that it's gonna be a 2v1 in your lane. If they are GOOD, they will spam gank other lanes (even if something like noc that normally wants 6 first) because they don't have to respect counter-gank potential for the most part. They should also accept vertical jungling; their jg on your side of map belongs to enemy; the enemy's jg on the other side of map should belong to your jg.
Build as much durability as you can to sustain 2v1 ranged harass in lane, and then focus on burst damage - as much as you can safely squeeze into your kit. Look for mistakes or openings where you can fight them under your tower and they can't fight back w/o tanking tower to get favorable trades. Or look to catch one w/o the other and use your burst to nuke them. It's not going to be enough to kill them, but you can force them to play more passively and delay their ability to truly come online. All this buys time. Time for your teammates to win 1v1 or 2v2 w/o much fear of being ganked; still need to respect potential for twitch jg to occasionally roam to other lanes. Time for your jg to snag every dragon and to snowball the other 2 lanes. You won't probably win 2v2, but you can win 5v5 and 4v4/4v3 while all you have to do is stall. If they can't snowball off killing you repeatedly and take you out of relevancy in levels and items in the game... they lose. So long as your team is pulling THEIR weight that is. Because you have 5 players on your team and they have 4.5 players on their team.
I was 1v2 chunking twitch or lulu for about 2/3 of their hp, surviving their full burst combos (including ults) and forcing them to base in exchange for me basing. We'd trade flashes. And all that time... my team could snowball bot, grab towers all over the map, and by the time we were fighting 5v5 over big objectives (mid game drags, baron, 5 man tower sieges) I was stronger than the lulu by far and twitch was no stronger than our adc... if not weaker. We destroyed their team 5v5. They couldn't split either... because I had waveclear, burst, and durability to stop them burning down towers 2v1. And my team easily won 4v3's. So they had no options. Because I played correctly against the cheese and because my TEAM played correctly. They didn't sit on their butts in lane forever going even or losing. Jg didn't afk farm for 20 min or try to contest enemy jg in top side where their "boosting" duo was. He went to lanes, snowballed teammates, got objectives, and used vertical jungling to stay even or ahead in jg farm (not overall farm).
We still kept wards out to spot when twitch would leave lane which.... protected my teammates from the odd gank or two AND let me abuse my "support" lane opponent when she didn't have over-farmed twitch protecting her.
Is the strat or others like it annoying? Yes. Does it illustrate how adc (or melee adc like yi) have too much power when combined with an enchanter support or someone like taric? Yes. But can it be beat regardless? Yes... if you AND your TEAM all play correctly and accept where you might be stronger/weaker and maybe need to adjust from your normal playstyle for that match (such as playing safer, different build order, vertical jg, more ganking, etc.).
support solo laner and a hyper carry jungler like 
Twitch/MasteYi and giving them all the farm and pretty often kills, this then turns into an unstoppable snowball ( an avalanche one could say ) that kills the thrill of climbing the ladder.
Nunu and 
Karthus jungle (both with 
) that allows Karthus to get lvl 6 while a midlaner is still 2 levels behind (4).
[leblanc-funny] 
