O31, O36 etc ratings. Are they reliable?

As far as diesel engines go, no the ratings from Lionel aren't accurate. Nearly all of the LionChief locos (before the advent of FasTrack) once came in train sets that included 027 track. Which means any of these locos that came in a set before FasTrack was introduced, will run on 027 curves. Obviously newer recently tooled larger and longer LionChief diesels like the Tier 4 probably won't.

Now one could make the argument (as some have here) that because Lionel no longer makes 027 track (or FasTrack with a 27 inch diamter), that the minimum curve would reflect this fact. But there some locos like the Industrial Switcher and the 4-4-2/2-4-2 steam engine that are still listed as 027 minimum curve, as well as many rolling stock items.

Steam engines are another story in part because of the LionChief tether plug connection. There have been plenty of threads here from folks encountering various problems with the current plug type tether, and not just on LionChief, but LionChief Plus too.

Also, you didn't state which steam engine you have, but a 4-6-0 could be one of the Hogwarts type of steam engines. Again, there have been threads here on that one including derailment problems and that it needs 036 curves to run correctly. If I remember correctly, the front guide truck hits the body of the loco on tighter curves.

Even with engines rated for 027 curves, sometimes you can encounter problems with the front guide truck derailing on "S" curves, or on turnouts right off curve tracks. I've solved that problem by either adding a self-adhesive weight  or a small magnet to the front guide truck.

As far as traction tires on diesels, where there are two, Lionel has always put them on the same side of one single motor truck, which I think is the best set up for tight diameter curves. K-Line put them all over the place: On front and back wheels on the same side, on both wheels of the same axle, and diagonally, one on the left and one on the right. Any diesel that has traction tires either on the same axle or diagonally, I remove one of them and have found I get much better operation on my layout that has 027 curves.

On my steam engines, there is only one single traction tire. But I can easily imagine encountering problems like you mentioned having two traction tires on each wheel set of the same axle. On the last printed Lionel catalog I have (the Ready To Run from 2015) the Hogwarts steam engine is listed as having 2 traction tires, and also with a 031 minimal curve... which is funny given how many threads there were here at one time about derailment problems.

@VHubbard which loco did you buy?  If it was the Hogwarts / English-styled 4-6-0, it's widely known that one won't run on O31.

All that being said, O36 is what Lionel has been including in their ready-to-run sets for several years now.  I wouldn't advise anyone to build a new layout with O31, unless you're absolutely squeezed for space.  If orange is the new black, then O36 is the new O31.  A widening of the radius was probably inevitable with increasing emphasis on scale-sized locos and rubber tires on both sides of the axle.  I just wish @RCSSTEVE would offer his excellent switches in O36 so we would have more choices in addition to the often noisy Fastrack!

If Lionel says it will run on X, it should. Sometimes you get wiggle room going smaller, tho. It’s not uncommon for O72 listed equipment to clear O60 curves. Or maybe O54 equipment to run okay on O48. Switches may be a different story, and you can run into other issues with the engine running, but maybe a tender or cars derailing. Mechanical stress is possible too, depending on how tight things get. There can be some trial and error especially with larger equipment.

It was the Hogwarts engine.  One more thing added to the "new to me" equipment prove out.  There was also the SD70MAC 18250 shorting going thru an O31 switch.  Fixed with 3D printed wheels.