Well, actually, I'd support Soljashy here. This topic is barely 18 hours old, jxh2154 - I don't think you can really claim that a consensus has been built.
忘れ物 has not "evolved from 忘れるもの". As it is formed with the stem of the verb, it has an entirely different meaning from the compound formed with the entire verb. 忘れるもの is a phrase composed of the head noun もの described by an attributive relative clause, 忘れる. 忘れるもの is "that which forgets". 忘れ物 is a verb-noun compound word, not a multi-word phrase. Its meaning is not set by any rules of syntax, but is just developed naturally in its specific case - in this case, it means "something that was forgotten". In other such compounds, like 流れ者, the compounding process forms in an almost inverted way, since 流れ者 means "drifter" (~vagabond).
うたわれるもの is very likely supposed to mean 謳われる者, but even if not, it is clear that うたわれる is a verb (probably passive construction of a verb written うたう), and that it is forming a relative clause modifying the noun もの.
Considering うたわれもの and うたわれるもの to be at all comparable grammatically is a mistake. うたわれもの, if attested, would be a single word, and うたわれるもの would be two words forming a phrase. Note that this conclusion is totally independent of the actual meaning of the words - it is wholly the result of syntactic, not semantic, analysis.
So Soljashy is totally correct, objectively. Of course, it's another matter if we want to drag the other 99% of danbooru kicking and screaming into calling things the way they should be called rather than the way that the vaunted "English-speaking anime community" tends to call them. Again, I'm all for this suggestion, but I don't want to get yelled and screamed at like back when I suggested ookami to koushinryou, either. So there's that.
EDIT: To those over whose heads the technicalities of grammar have been flying, I would like to mention that pretty much all "grammatical evidence" mentioned earlier in this thread has been rather vague and unsuitable (imo) as the basis of any kind of policy. Soljashy, whether something is a "single concept" or not is immaterial, not to mention very difficult to define properly.
richie's speculation about passive verbs + nouns and supposed etymology is nonsense. Ancient feeling of the title? What? I would like to suggest that you learn Japanese a bit more before attempting to invoke grammar that you don't understand. Nothing personal.