I wouldn't worry too much.
My own MIL announced that she would be moving in with us when she was older & needed extra care. We were literally just married & like your situation it made no sense at all as DSIL lived really close to her, we didn't & she did a lot for MIL already. Plus DSIL lives in a huge house with dozens of bedrooms & a bungalow wing & we have lots of stairs.
Turned out MIL was peed off with SIL as she was "bossy" simply because SIL was worried about MILs health & kept trying to get her to stop smoking, so MIL decided that I was a softer touch & wouldn't boss her around, plus I cook, SIL doesn't & MIL liked my cooking, so it turned out to be a compliment in a way. DH was horrified too, but soon made it clear that nobody smokes in our house either & she was being unkind to SIL who was only bossy because she cared.
Roll forward a lot of years & MIL stayed in her own home, close to her friends, SIL arranged carers to go in daily for her & saw her 3/4 times a week for more quality time. DH travelled to see her twice a week too & we went with him at least once whilst we still could (DD was seriously ill) I did cook MILs favourite pies & stews from time to time & DH took it too her.
In the end, bar daily phone calls, which we all enjoyed, MIL didn't expect any of it, from any of us & really wanted her independence & own home, she died in January this year, loved her to bits in the end & still regret that we circumstances meant we couldn't see her much in that last year, as both DD & her were just too ill to travel.
It will be fine, if she mentions it again, pull her up on it, by pointing out that its a bit unfair to SIL who obviously cares so much & why on earth would she think such a thing