may have been busy without a time adverb

[kwfine]

Dear teachers,

(1): The postmen may have been very busy
(2): The postmen may have been very busy recently / since yesterday

A friend of mine said it is completely incorrect for me to write (1), so I wrote (2) instead in my composition.

I am wondering whether it is incorrect if I just say "The postmen may have been busy" without a time adverb.

Thank you.

Kitty

[Alan]

Not in the least! Such time adverbials can be understood from context.