This is where cultural differences lie.. For you this is a "business Transaction" for many cultures this is called "taking care of your own" and how family works.
This situation is not "taking care of your own". It is a business arrangement and one that may have zero benefit for the IL's outside of having a place to live. I have no idea what the costs will be or what that amount translates to for the iIL's or for the OP, but I can bet you dollars to donuts that if this arrangement did not work out, each party would have the cost down to the penny burned into their brains.
OP- if you want to open your home to yoru IL's, and if that entails renovating your basement then I would suggest you assume the cost of the renovation and expect that that cost is yours alone. If the IL's decide to move in, then the financial arrangement whole they live there could encompass the cost of the renovation, but call it what it is: Rent. Be sure you can afford the entire package on your own, and that if the IL's decided this arrangement was nto working out, or if they decided FLorida was calling them, that you woudl not be upset paying for your newly finished empty basement apartment.
My DD and DSIL lived with us for several years while they saved for their own home. It was not a perfect arrangement, but it was a good one. You know upfront that both families are giving up privacy, and you know that both families are compromising their lifestyles to be together, but knowing something and actually living that are two different things and you will not knwo if both of yoru families can make that compromise.
It seems to me that your MIL already has some concerns, and she may know a bit more about this kind of compromise, and how you all may react once this plan is in place than she wants to share for now.
My DH loved having our DD and her family with us and he really would have moved Heaven and Earth to add onto our home and have them stay indefinitely. (He adored our DGD then and does now still) however once he started mentioning that, DD and DSIL hotfooted it to the nearest REaltor and bought their home, and I did not blame them. For them, and for me, there was a difference in a temporary arrangement that was working well for the most part, and a long term commitment to giving up the majority of your privacy and control over many of your decisions. I think the best thing they did for them was to make that decision to move on, because their little family unit just got closer and closer, which is what we both really wanted for them.
For your IL's, if they agree to this long term plan, complete with a financial commitment, in writing or not, they are agreeing to give up a lot of their autonomy in order to have a home with you. If things go belly up there is a solid chance that their relationship with their daughter may suffer, so think long and hard how you approach this.