Wobble and steering wheel shake - odd source

[MikeReilly]

Recently our 2010 base vibe has developed a low speed wobble somewhere in the front end. Here's the story along with the fix.

At low speeds, we have been experiencing a significant wobble in the front end that you can feel quite noticeably, not just in the steering wheel, but also causing the whole front end to shake a bit. It evens out to a vibration at higher speeds and isn't very noticeable then. Thinking that this must be some kind of steering/suspension issue, I've jacked up the front end a couple of times to check ball joints, tie rod ends and bushings, but no joy despite a little bit of a clunking noise at times while driving at lower speeds. On a hunch, I decided to put the snow tires on and see what happens. Guess what? Symptoms disappear. One of the tires has very slight deformations in the side wall, so I'm assuming that some of the cords inside have snapped. I would never have thought that a tire that wasn't obviously buggered could lead to such noticeable symptoms, but there it is. As the tires were down to about 30% and we are planning a road trip to Mexico for a few months, we had already ordered new tires at Costco.

[Caretaker]

The tire wouldn't happen to be one of Michelin's infamous BF Goodrich T/A tires, would it?