I don't know exact specifics of typical PM agreements, but usually yeah the PM follows whatever the landlord specifies. If the PM doesn't like the landlord's terms, they will just decline to do business with them, but ultimately they're just the landlord's agent.

I'd hazard that the PM charges a percent of the gross rent, but has a minimum irrespective of the rent actually charged, so the landlord will then just tell them that they don't want the PM to rent at a price where the PM's minimum fee is more than the fixed percentage. (or in hard numbers. If the PM requires the greater of 10% or $100, then the landlord will just say "don't rent below $1000")