Hmmm. I'll try and be a bit clearer about it
I didn't say that consider *was* wrong, I said it sounds wrong to my ear. You could use it and it would be perfectly
understood, but I also don't think it would be the natural choice for a native speaker. This is an interesting question, it's making me really think. One of the things I love about English is the wide vocabulary which really allows for shades of meaning, but of course that is one of the hardest things for a non-native speaker! Thank you for asking the question.
When you consider something, the outcome of that consideration is (usually) an
opinion or a
choice. You make a judgement about which soy sauce you like the most, or which girl is prettiest, or perhaps after considering all the options, you decide you will do X instead of Y. "Considering" something allows for the fact that other people may disagree with you, or that other people would have made a different decision as the result of their own consideration process. In your examples above, the speaker(s) are allowing the possibility that someone else might blame the person/not think the speaker has been totally vindicated/think the arrangement is perfectly practicable etc. It's not really possible to
prove any of the opinions
In your original sentence, the question you are faced with is a matter of *fact* not opinion, either passwords have been lost or they haven't, so, to me, consider doesn't really fit the situation. If you want to use consider, to reassure your membership that you are taking the matter seriously and have spent time thinking about it, you could try saying:
as, having considered the situation, we believe/suspect that other passwords have also been lost.
This would be using meaning (1) of consider as defined
here.
In order to use "consider" in place of believe or suspect and have it sound natural I think you would need to change "have also been lost" to "may have been lost" to open up the possibility they haven't been lost a little more.
as we consider that other passwords may have also been lost.
I still don't like it very much though, if I'm to be 100% honest.
I'm sorry there isn't really a simple rule I can point you to here to help, but this is all to do with subtle shades of meaning; I think your standard of English is good enough to take it though.