I certainly wouldn't give the rear axle a 2nd thought. I saw you said it was fine. Personally I don't trust a dealer with not one word that comes out of their mouth. I have 1 shop ... just ONE, that I actually trust to tell me the truth about the alignment condition. And it's only because I just happened in their shop.
I have a 2003 Camry (that is the best car ever). It had about 80k miles on a set of michelins. Maybe more miles that that. The front tires were plum worn out. And they looked worn out more either on one side or on the outsides ... I forget. The Discount Tire guys nearly freaked out, "oh you gotta get an aligment, RIGHT NOW." But I told them, those tires have 10 million miles on them, and the car still drives quiet. No shimmy, no shake, no pulling either direction, steering wheel is straight ... it doesn't even feel like the tires are worn. It drives like a cream puff. "Doesn't matter, those tires are being chewed up."
I didn't believe them really, so before I bought tires from them, I take it to the shop next door (because for some D/A reason Discount Tire doesn't do alignments). That shop put it on their 4 wheel alignment, then called me in about 45 minutes and said ... "hey, we could charge you $92 and adjust your alignment and try to make it straigher ... and probably make it worse ... but that car is straight as an arrow. No alignment needed. What do you want to do?"
I told them that not only do I prefer to save $92, but for their honesty, I'll take a set of 4 tires from you. I've been using them ever since. I get really intimate with my vehicles, and I can feel what they need. Took my dad's pickup (which is now mine) to them, and they diagnosed exactly what I was feeling with the truck.
Point is: I doubt your dealer is fibbing about this particular issue. But I also doubt your vehicle has any axle issue to be concerned about. But in the future ... unless a check or repair is covered by warranty, find yourself an outside shop that you can trust. I worked in design for Toyota and Hyundai. I got some direct work with dealers with Hyundai. And they (and probably all other OEM dealers) are the most deceitful, incapable sons of (you know what) that ever walked the earth. They make Las Vegas casinos look like Bible School classes. My $0.02 worth.
7milesout
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View my fuel log 2020 Mirage ES 1.2 manual: 42.4 mpg (US) ... 18.0 km/L ... 5.5 L/100 km ... 51.0 mpg (Imp)