As other answers have said, if it isn't confirmed in writing, then it isn't contractual. End of story.
I don't buy that she can't get it done because (whatever woo woo explanation she may have given). A system that doesn't let people fix errors in their written letters and contracts? Despite "trying everything"? Hmmm.
I'd handle it this way:
- Ask her more specifically, what is the problem. What has she tried? This is for background and to see if it's plausible.
- Ask her, is she saying then that it should say permanent, and the employer agrees its permanent, and it says so on the system?
- Double check her answer, "So the employer says its permanent, its just a printout issue of some kind?"
- Then finally, "Fine, in that case I'd like a 2 line letter or email from the employer just to confirm for the record that it is correctly understood as permanent, and that the offer statement that it's short term is incorrect."
You need it from the employer not her, because then its enforceable as part of your contract with the employer, and they can't shrug it off as an incorrect statement by a third party.
What will happen, she will either say "sure" or "I'll ask and see what I can do", or she will come up with instant excuses why they won't do that, or can't do that, or you don't need that.
If she says "fine!", then let her get on with it. She either gets you that email/letter or fails. If she fails, see below. If she succeeds, make sure its from the employer, not just from the agency or on the employers behalf. You want the employer to confirm it, themselves.
If FOR ANY REASON ON EARTH she doesn't. Or its not signed and sent by the employer themself. Or they can't or won't. Or she doesn't want to disturb them. Or its taking inordinate time or the right person isnt doing it. Or ANY OTHER REASON ON THE PLANET. Or ANY OTHER OUTCOME ON THE PLANET OTHER THAN EXACTLY WHAT YOU ASKED FOR.....
Then be as tactful or as scathing as you like, because games are going on.
They want to recruit you, they (allegedly!) agree there's a mysterious error that the employer wants to say perm but somehow can't fix it, and yet the employer somehow can't agree or manage to write a 2 line letter/email to say "Dear Name, please disregard short term it should say permanent, in your contract, and amend your copy. Yours truly"?
Bullshit. Leave and make clear in a totally professional way that you do not feel the trust that you would need, to take up the offer. Or if tactful is your style, that in light of their inability to produce a 2 line email from the employer confirming what they say the employer totally agrees to, and agrees is mis-printed, you are unable to.
They'll get the idea.