I wouldn't think that would be the case. 32Gb isn't that big. Many of us use 64, 128, 256 pretty routinely
I've got thumb drives up to 8 TB that work with everything I've tried including my Samsung TV. Sounds great but it's a bit bigger than Big Lighter which is ok I guess, but too darn slow (very slow). I'd rather have 1 TB that's fast but had to try one as they were 50% off on Amazon. Should have been 75% off.
The problem is likely that it wants Fat16 so maybe just reformatting the existing thumb drive at any size will allow the TV to read the thumb drive correctly.