Moser Shtarosav L'Bais Din

In Meseches Makkos there is a machlokes between Rashi and Tosafos regarding moser shtarosav l'bais din. As we know the shmitah year cancels all loans. Hillel was mesaken something called a pruzbul whereby a person can essentially make Bais Din the baal din on his loans. By doing this, shmittah no longer cancels his loans. The gemara in Makkos says that one can "give his shtaros to Bais Din" (moser shtarosav l'bais din) in order to avoid the shemittah cancellation. Rashi says that this terminology [of moser shtarosav l'bais din] is just another way of saying pruzbul.
Tosafos, however, argue that pruzbul and moser shtarosav are two separate things. A pruzbul is an enactment of the Rabbis. However, when one actually gives over his shtaros to bais din, this is a d'orayssa halacha. In this case, min haTorah, the loan is not cancelled.

Here is how the Rambam brings the halacha of moser shtarosav l'bais din:

[טו] המוסר שטרותיו לבית דין, ואמר להם אתם גבו לי חובי זה--אינו נשמט: שנאמר "ואשר יהיה לך את אחיך" (דברים
טו,ג), וזה בית דין תובעין אותו. וכן בית דין שחתכו את הדין, וכתבו איש פלוני אתה חייב ליתן לזה כך וכך--אינו נשמט: שזה כגבוי הוא, וכאילו בא לידו; ואינו כמלווה.

The Rambam brings down the case of moser shtarosav and quotes a source in the torah for the fact that shemittah does not cancel institutional loans. The simple implication of the Rambam is that moser shtarosav l'bais din is a d'orayssa concept and is separate from the concept of Tosafos. This is the way the Mahari Kurkus learns the Rambam.

I saw a strong question on this Rambam. We mentioned in this post that the Rambam has a unique shittah, that shtarei mamon only exist on a d'rabbanan level. On a d'orayssa level a shtar wouldn't work because it would be a problem of mipihem v'lo mipi ksavam. If all shtaros are, in fact midrabbanan, how could the Rambam say that moser shtarosav l'bais din is a d'orayssa?