You know, I think that if the daycare provider feels that she can keep him contained on the mat, that's a great idea.
Just to expand; there is a child development approach called 'Reggio Emilia' which originated in Italy-- there, babies actually sleep in these neat baskets they can crawl in and out of, to encourage autonomy (The child does not depend on the caregiver for sleep/waking cycles or to be taken out of a crib. It's like a larger Moses basket, only there's no wall at the foot...
(I tried to find an image to share, the baskets are lovely, sadly could not.)
If you are worried about him being underfoot of the bigger kids, talk to the care provider about how she might keep him safe. Or accept the ruling and just use the porta-crib's mattress... plenty of kids have slept in the porta-crib and have slept well.
ETA: I also have to agree wholeheartedly with Bug-- be glad that your care provider sought a license or a permit and is doing things by the books. So many family care providers don't.