All it takes to use an Inquisitor in your kill team is a little ingenuity and roleplaying - plus, a GM that can say "no" and have it stick. Rule number one: The GM is always right.
First of all, the Deathwatch works at the behest of the Inquisition in the first place - meaning that there is usually more than one request for their help at any given time. Make the Inquisitor spend his or her Influence in order to actually recruit the Kill Team!
Second, unless the Inquisitor has a private stash of Astartes-issue gear, his or her Influence will get exactly nowhere when it comes to procuring gear for the Marines. They can only get what's actually in the Armory, which is usually limited. If you don't want the Kill Team to dress up in Terminator Armor and wield mastercrafted Plasma cannon, all you need to say is that those suits the company does have are already fielded by another team working for an inquisitor with larger influence.
Third, most of the time those Inquisitors who actually get down and dirty with the Marines are too busy to actually do all the political wheeling and dealing to acquire excessive Influence. Those that do have big influence might need to stay undercover and thus be unable to excert much of it due to the risk of getting caught by the enemy.
Fourth, the Inquisitor has other things to do than ride herd on the Marines all the time - separate him/her from the group if you think they need an opportunity to use their own social skills. The player might enjoy a bit of DH-style solo adventuring from time to time, otherwise they wouldn't have chosen an Inquisitor to play as. (The rest of the group can roll some non-combat acolytes if they don't want to get left out of this plot…)
Fifth, an Inquisitor having more diverse and powerful psyker powers than brand new Deathwatch Librarian is not surprising - up until joining the Deathwatch, the Librarian has lived a mostly regimented life with little chance for independent action, due to being low man on the Librarium Totem Pole. The Inquisitor, on the other hand, has been thinking on her feet for years already, and has developed some tricks of her own that didn't come from books…