I'm not completely up on Halo lore, but humor me for a minute.
Let's assume for a minute that Lone Wolf is a Spartan III. (Again, humor me).
If Lone Wolf is a Spartan III wearing a Mjolnir armor variant that appears to be similar to what Spartan II soldiers wear, what makes everyone so sure the rest of Noble team are Spartan II soldiers? They're wearing Mjolnir, but if Lone Wolf is a Spartan III and can wear Mjolnir, why can't the rest of them also be Spartan IIIs?
I was under the impression that Spartan IIs only had numbers up to 150, and yet Kat and Carter are 320 and 259, which furthers the speculation that they're not Spartan IIs.
In fact, Jorge who is number 052 and therefore more likely a Spartan II is much larger than the rest of Noble team. Relatively speaking, the rest of Noble team seem smaller, which makes it more likely they're Spartan IIIs as well.
So what's up with that?
Not to derail too much, but as someone else mentioned, I highly doubt that the press release would have a typo that would say "Spartan III" when it should have said "Spartan II" because they haven't ever mentioned Spartan version numbers in past press releases. Essentially they would just say "Spartan" and leave it at that.