Here's an example based on AmaiKotori's answer. I edited and tweaked it down a bit to prevent spoilers since it's the very opening, but it will be recognizable to anyone who's read the novel in question. The novel and author name is down below.
Special Agent Alpha, stood in the doorway of a cheap, rented
room in a lower middle-class section of town near the Docks. The door
was open, and a man lay on the floor with a large, heavy-handled knife
in his chest.
Along the right-hand wall was a low bed. It was
made up, but the wrinkles in the cheap blue bedspread indicated that
someone had been sitting on it—most likely, the dead man.
back down at the body. Then, cautiously, he closed the door behind
him, stepped over to the supine figure, and took a good look. He
lifted up one hand and felt for the pulse. There was none. GB was dead.
He took a step back from the corpse and looked at it thoughtfully. In
Alpha's pocket was currency, money which had been
drawn to pay GB for his services to the Agency. GB, he thought to himself,
would no longer be any drain upon the special fund.
He stepped over
the body and looked at the papers on the wooden table at the far
corner of the room. Nothing there of importance. Nothing that would
connect the man with the Agency. Nonetheless, he gathered them all together
and slipped them into his coat pocket. There was always the chance
that they might contain information in the form of coded writing or
The small closet in the right-hand corner of the room,
near the door, held only a change of clothing. Nothing in the pockets,
nothing in the lining. The two drawers in the closet revealed nothing
but underwear, stockings and other miscellaneous personal property.
Again he looked at the corpse. This search would have to be reported
immediately to the Chief, of course, but there were certain things
that it would be better for the local police not to find.
The room had
revealed nothing. Since GB had moved into the room only the day
before, it was highly unlikely that he could have constructed some
secret hiding place that would escape the penetrating search of Alpha. He
checked the room again and found nothing. A search of the body was
equally fruitless. GB had, then, already dispatched whatever
information he'd had.
Alpha looked around the room once more to make absolutely
certain that he had missed nothing and left.
What the reader is apparently reading is the story of a spy, sent to meet a contact (and pay them), finding the contact dead, and then sanitizing the room to make sure there was nothing to reveal that the victim was an informer.
What you're actually reading, and don't realize out until the end of the story when the protagonist reveals the plot the murder was a part of, is that this scene starts seconds after Alpha had just stabbed GB with said knife. He was checking to make sure he was dead, make sure there was no other witnesses, and not only making sure there was nothing to connect the victim to the Agency, he was making sure there was no evidence for the local cops to find connecting GB to him.
At no point is the author lying about what's going on or what's in the viewpoint character's head. They're just not giving you the entire context of what's going on. The details they've added about the search, and why the search and removal of possible evidence is occurring, is entirely understandable to the reader and justified and plausible from an in-story standpoint as something that character would do. They're just not saying it isn't the only, or even primary, reason the character is doing it.
The novel is the Lord Darcy novel Too Many Magicians by Randall Garret.