Can "believed" ever be an adjective?

The ti­tle ex­plains it all. I had an ar­gu­ment with my English teacher; she gave us a task to con­vert nouns to their cor­re­spond­ing ad­jec­tives and verbs.

She gave us be­lief as the noun and told us that its cor­re­spond­ing ad­jec­tive should be be­liev­able. I think that’s true, but I thought that be­lieved should also count as a cor­rect an­swer as well.

Am I wrong?

For example, is it wrong to say the fol­low­ing?

It is a gen­er­ally be­lieved fact.

Or should be­lieved, for some rea­son, not count as an ad­jec­tive in that sen­tence?

From the four criteria considered to be the common characteristics of adjectives (CGEL § 7.2 p. 402), can be concluded that "believed" tends towards the status of a full adjective but that its use is subject to much idiomatic constraint.

A) attributive function: Yes but rarely unmodified and if so noun sensitive¹
B) predicative function: Yes but idiomatically restricted
C) modification by very: No
D) comparative and superlative form: Yes but idiomatically restricted

"Believed X" used if X is one of the following: story, tale, principle, notion.

(generally believed fact)

A (2014 - believed proposition) Our paradigm for such basing is the case in which we make a conscious inference from one or more believed propositions to another one.

D (2012) In the relative sense, then, the sense in which we contrast reality with simple unreality, and in which one thing is said to have more reality than another, and to be more believed, reality means simply relation to our emotional and active life.

B (2012) . were more familiar and more believed than any of the identified folk beliefs.

D (2010) as to render the metal of our true English valour to be the more believed and feared abroad,

B D (1760) But his dying so “ critically , as it were in the minute in which he seemed " to begin a turn of affairs , made it to be generally the “ more believed , and that the papists had done it , either " by the means of some of lady Portsmouth's servants , or ...

D (2012) In the relative sense, then, the sense in which we contrast reality with simple unreality, and in which one thing is said to have more reality than another, and to be more believed, reality means simply relation to our emotional and active life.

B D (2014) A speaker who can look a person in the eyes when speaking with them is more believed and trusted.

B D (1820) .. and the state or necessity “ of Bishops be more believed.

B D (2010) The more specific the praise is, the more believed and appreciated it will be.

A (2008) I do believe there are more believed lies told in June than any other month—

This reference shows that "very believed" is considered to be incorrect: 1981 - Lexical Rules of Semantic Interpretation: Control and NP Movement in English and Polish.

¹_{Observation due to user Edwin Ashworth}

Dictionaries are often and notoriously incorrect when it comes to part-of-speech designations. However, when the Oxford English Dictionary ("widely regarded as the accepted authority on the English language") speaks, people listen. Perhaps your teacher will too.

Here's what it has to say (along with a couple of the usage examples given):

believed, adj.
_{Origin: Formed within English, by derivation. Etymons: BELIEVE v., -ED suffix¹.
Etymology: < BELIEVE v. + -ED suffix¹.}

Relied on or trusted in as a matter of faith; accepted as true, accurate, reliable, or really existent. Also believed-in.

_{1983   P. TAYLOR Limits of European Integration vii. 227   Attempts to improve standards merged imperceptibly into activities to promote the Communities at the believed ‘expense’ of the states.
2007   J. SØRENSEN Cognitive Theory of Magic ii. 29   Magical actions rest on a believed identity between symbol and the symbolised prevalent in traditional societies.}

_{Source: Oxford English Dictionary (login required)}

Believed can act as an adjective as any particle can. The really crucial point is that as such, since believe means:

to think that something is true, correct, or real:

it means "to be thought true, correct or real," whereas believable means

belonging to a type that seems real; realistic:

Hence, something can be believed while not being believable (to an objective eye) because the believer is credulous, and vice versa, as when a malicious person believes anything bad that can be said against people, without evidence, and nothing good, regardless of evidence.