It's really easy to blind a variable time modular inverse, assuming you have a random number generator handy: you want the inverse of x, compute instead the inverse of x*r, then multiply the result with r.

So I wonder if some things using the same chip/library are not actually vulnerable because they blinded the operation?

It's *better* to use a constant time algorithm, but that's harder to do in a curve generic way and has a pretty significant performance impact (particular before the safegcd paper).