They may not have needed to rent a facility for the Trump Administration documents, they probably already had a facility. If they didn't already have space, of course they rented it. Where do you think the NARA is storing the stuff that the Trump administration did turn over?
And yes the NARA moved all Presidential Records that the Trump Administration turned over (probably under GSA contract) from the work location to where ever they are storing the Trump Administration materials.
The fact that the FPOTUS (had his team) box materials and move them to MAL outside the scope of the NARA so as to not comply with the PRA of 1978 is on the FPOTUS, not the NARA since the materials were not turned over as the law requires.
So the NARA somehow forced the FPOTUS not to comply with the law?
WW