First of all, you shouldn't use the term "subject" or "object" when talking about active vs. passive voice. These terms are ambiguous since they are changed when the voice is changed. "Agent" is preferable, but at least you need to make it clear by using "subject in the active sentence" if you use those terms.
It seems to me that where で and に used with Japanese passive verbs do not always translate to "with" and "by" in the English counterparts.
I didn't say such a thing. That's not my point at all. It is common knowledge that a particle in Japanese is not in one-to-one corresponding to a preposition in English, needless to say. I just said that your question was like my parable, as if it's like a question of a learner who is confusing different functions of prepositions in English.
I would still say the crow was chased away BY rather WITH the falcon even though で is used in the sentence. I guess that に can be used instead of で in this case, can't it?
"Those two sentences are almost the same in meaning" doesn't (at least not always) mean "で can be replaced with に" and "the function is the same between で and に in that sentence". Indeed, there are cases where the difference can be considered to be just a nuance as a result, like 毛で覆われた vs. 毛に覆われた or 家具で囲まれた書斎 vs. 家具に囲まれた書斎, but "there are cases where に and で seems to be interchangeable in a passive sentence almost without changing the meaning" is not the same as "に and で are the same in the function in those sentences", of course. You need to realize a simple fact that に and で are different particles in the first place. に indeed can be used there, but 駅前のカラスが鷹
で追い払われた。and 駅前のカラスが鷹
に追い払われた。are not the same in meaning, as I explained below.
How do you interpret ウイルス
に入国を拒否された。, by the way? Why に can't be used here? (Although it's grammatical, the meaning is clearly different form the original.)
Having seen your examples of active voice converted from the passive counterparts I tentatively conclude pending your opinion that で goes only with noun that can't be a volitional subject when the passive verb is converted to active verb. I don't know what else I can base it on.
Why do you think that those active sentences are derived from the passive ones? Isn't it possible that the active ones are the original? No one can say which is original since both are equally possible. (More precisely, the idea which is original is non-sense.)
Also, are you saying that で can indicate the agent when it's volitional? You yourself said "I see that the noun that goes with で is not involved in a subject and object relationship in the two sentences.", no?
You seem to be still misunderstanding. The noun indicated by で is
not the agent (= the subject in the active sentence), as I explained so far repeatedly. Seems like your sticking to the idea "で can be used to indicate the subject/agent in a passive sentence in some cases" is the key of your misunderstanding and confusion in this case. I have to point out that the problem is on your way of thinking also here again. It's not "で is used to indicate the agent in a passive sentence instead of に", but "unlike に, で is not used to indicate the agent in a passive sentence. で is actually used for other functions such like to indicate material, means, cause/reason, etc., as same as in an active sentence". This is a fact. Whether or not you insist that it seems
to you that で can indicate the agent in a passive sentence, it's simply wrong.
See the following sentences. These examples are clearly show that ウイルス and 鷹 are actually not the agent, right?
入国管理官にウイルスで入国を拒否された。
駅前のカラスが鷹匠に鷹で追い払われた。
cf. active version
入国管理官がウイルスで入国を拒否した。
鷹匠が鷹で駅前のカラスを追い払った。
Would they be alright that the verbs be rendered into passive form?
That is as follows.
毛に覆われた表面
家具に囲まれだ書斎
泥棒に盗まれた財布
Yes, of course, but I don't understand why you need to confirm it. It's obvious, as you can see those examples in this thread, no?
に indicates the agent in the passive sentence.
↓
therefore
↓
に can't be used in the counterpart active sentence, as in the three examples below, since に can't indicate the agent in the active sentence.
×毛に覆った表面
×家具に囲んだ書斎
×泥棒に盗んだ財布
で doesn't indicate the agent both in the passive and active sentence.
↓
therefore
↓
で can be used also in the active sentence without changing the function of で.
〇毛で覆った表面
〇家具で囲んだ書斎
(で can't be used for 泥棒 in the active sentence since, unlike other examples, the agent is the only one possible function of 泥棒 in the example 泥棒に盗まれた財布/泥棒が盗んだ財布, and で can't indicate the agent in an active sentence.)
This is applied to other examples in this thread, of course.