Allege: claim or assert that someone has done something illegal or wrong, typically without proof. to say someone did something wrong (no proof). "His stories included an alleged cover-up of infections, and a busy crematorium." Alleged is used as an adjective to describe the cover-up (someone has accused them of covering up infections and this is wrong - no evidence) "They allegedly worked as government intelligence officers." Allegedly is used as an adverb to describe the verb

When you “make an allegation” against someone it means “to say that someone has done something wrong but it has not been probed and proved yet.” We usually use “alleged” or “allegedly” to state that there is a belief over a wrongdoing but there is no legal confirmation to it. Oftentimes, allegations are taken to the court for investigation, but not necessarily.

Allege does mean to state but it means to state without proof. In your first sentence, the cover-up hasn't been proven yet. In the second sentence, allege is used to show that the writer doubts that they actually were officers.