The following example is taken from source
A：We saw a police helicopter overhead yesterday morning.
B：Really? They would have been looking for those bank robbers.
The website says that it is an example of usage of would to express an assumption, presumption or expectation in the past.
As this post indicates, the example here does not mean a hypothetical scenario or a past future tense, but a speculation about a past event.
I'm wondering whether the post was correct in explaining such usage. Please share some wisdom!
Only a few grammar books say "would have + past participle" can be used in this way. The following are a couple of the sources I could find, but I don't know whether they are reliable to believe.
Would + perfect. This use of would signals what we expect somebody to do:
John would have scheduled the meeting.
In this case, it tells us that the speaker expected John to schedule the meeting. We do not know if John actually scheduled the meeting.
-- McGraw-Hill's Essential ESL Grammar, for Intermediate & Advanced ESL Students (2008)
One of the children offered to help. That would have been Julie. (assumption about the past.)
-- Mastermind Use of English