It's actually not as improbable as you think! One simple factor makes it happen so easily: a speed steroid.
One of my most well-remembered moments as Yorick was when i was chasing down a Nasus. I activated both Omen of War and my Youmou's Ghostblade at the same time. I was running so fast, that not even Wither's 60% slow with exhaust was able to significantly slow me down, and I was still catching up with Nasus, who had no speed enhancers himself.
Here's an important thing to remember: when movement speed gets above a certain amount, a soft cap is applied onto it. Straight from the wikia:
If the raw speed is 415 or under, no cap is applied.
If the raw speed is between 415 and 490, final speed is soft capped to RawMS × 0.8 + 83.
If the raw speed is above 490, final speed is soft capped to RawMS × 0.5 + 230.
My "RawMS" was well above 490, but the softcap brought it down significantly so I wasn't running as fast as I "truely" would have without the softcap.
When Nasus used his wither on me, it brought me down below 490, meaning the soft cap slowing no longer existed. His slow amount was countered by the additional speed I got from having my speed reduced, paradoxically.
The same thing happens when I'm playing Yorick against Singed. His poison often is insufficient to slow me down enough once I have Omen of War out. But I don't ever ever try running through the smoke. Kiting is essential to defeating Singed, and as Jax, having no speed modifier means that kiting is your only tool to defeat him. Things to remember:
-If you can avoid engaging him while he has the insanity potion active, avoid it. Do not chase Singed. Do not chase Singed. Never chase Singed. No matter how low Singed is, you NEVER chase Singed.
-I talked to my brother, who mains Jax and has no trouble against Singed players. He advices that you need to be as defensive as possible against Singed until you hit level 6. Once you do, your attack order is to activate dodge, run at him, land the stun, give him some good whacks, and jump out before he can retaliate. Avoid jumping at Singed for initiation, because otherwise he will just flip you backward and start his slowing and you will take a brutal beatdown before you escape.
Defend, kite, build MR, only ever engage with Grandmaster's Might, and don't chase. These are the ways to defeat Singed as Jax, or as any top really. Those are the same three strategies I used when I play Yorick as well, although I'm fortunate that Yorick can move so fast, that I can usually kite Singed in front of him away from the poison.