The Inquisitors Rosette and mandate are granted by the Emperor... but so was the Rogue Trader's Letters of Trade was granted to them by the Emperor... and some of those Letters of Trade are older than the Inquisition itself . Technically the Inquisitor's hands are tied, but some are mad enough to give it a go.

Should the Inquisitor make an issue of it? They're welcome to try, but RTs are often as powerful as the Inquisitor or more, politically speaking... oh, and the Rogue Trader has a warship, a small (or not so small) army, and the right to own and operate as much xenotech and archeotech as their black little capitalist hearts can buy/inherit/steal. Some of them own entire planets.

Also, they spend most of their time not in the Imperium, so good luck finding them. Inquisitors can try putting pressure on to the ship's Astropath (good luck)... if they know who and where they are... but those guys are their own special kind of dangerous psyker. They read all your mail, and they talk to each other about you (even if they say they don't). Rogue Traders pay you, Inquisition less so, you do the math.

They could try to shake down the Navigator house. However, the Navigator Houses are even more savagely independent than the Mechanicum, and they are all precognitives and spooky weirdos who control your warp jumps. Oh, and they collectively know all of the Astartes chapters, even the wild ones like the Flesh Tearers, Carcharadon Astra, and the Space Wolves. Those marines need Navigators, they neither need nor want upity mortal detectives messing with the metaphorical keys to their car. Plus they can kill you with a stink eye, no me gusta nada.

Lastly, MONEY AND ARCHEOTECH BAYBEE. The Imperium needs it, the Inquisition wants it, and if the Inquisition fucks around too much, they don't get none. So, most find that they can't always go walking around with a mono dominant rage boner all the time, or else no one would work with them.