The gist is that the agency is going to demand a fee for bringing you in. A lot of times it’s a percentage of your offer. Thus, you get a smaller offer to offset or reduce the cost.
As a hiring manager for 15+ years, I’ve never nerfed someone’s offer because they came from an agency, nor have I ever caught a whiff of this happening.
I am conscious of which roles I offer to outside agencies, but once I do, I stop worrying about the cost and focus only on the value I can get from the candidate. Those agency roles are some of the most competitive positions; I don’t expect to be able to hire the best who happen to not realize that $0.75x is smaller than $1.00x for positive values of x.
I always thought it was because the recruiter only cares about whether you accept the offer, not really how much the offer is, and so will either negotiate based on that, or else pressure you to accept whatever offer they can muster. Plus, if the recruiter can bring in people who accept lower offers they're more likely to be used by the employer. Hence, if you accept an offer through a recruiter, it's likely that you're accepting a stunted offer.
Businesses always offer you the lowest offer they think you will accept. They can't offer you lower than you will accept, because then you won't accept it ;-) They will never offer you more than they have to just because they didn't pay a recruiter. Don't worry about that stuff, it doesn't factor into decision making.
I am conscious of which roles I offer to outside agencies, but once I do, I stop worrying about the cost and focus only on the value I can get from the candidate. Those agency roles are some of the most competitive positions; I don’t expect to be able to hire the best who happen to not realize that $0.75x is smaller than $1.00x for positive values of x.