My comeback would be "Well, she's fine to go to people normally, I don't know why she gets so upset with you?" (to MIL, that is).

Perhaps she's just a really good judge of character (not of your BFF, who I'm sure didn't make any snide remarks).

FWIW my DD was very attached to me and for some reason cried her eyes out whenever she saw MIL. I put it down to the way MIL was with her (very 'in her face', over-excitable, plus the fact she didn't see us for 5 mths, but that's a whole 'nother story) and the fact she had a very strong connection with me. She still has a very strong attachment to me, but is completely happy to go off and be independent at preschool, etc.

It's been proven that a strong attachment with Mum (and Dad, but to a lesser extent at this age) leads to greater emotional security as your baby gets older. You can tell her that if you're feeling more diplomatic!