Yes, this is true. Its the protein in the saliva, not the dander, as such. But dander is covered in saliva.
OP, my DS was extensively allergy tested as a toddler, and is v v allergic to cats. I know this is only anecdotal, but he ended up in hospital twice, ( once during a holiday cottage stay, where there had been a cat staying the week before), and once after a half hour visit to some friends. This was on the back of regular, well- controlled asthma inhalers.
He started off sneezing violently, within minutes, each time, and despite rescue inhaler medications being administered immediately, his eyes and lips swelled, he started wheezing, became short of breath, and was in hospital for 48hrs on oxygen, bronchodilators and intravenous steroids. This, with no direct contact. It was v frightening, and rapid.
I would be very wary, indeed.
He is 26 and still hideously allergic.
He's also allergic to rabbits, horses and donkeys.
It's a shame, as he really likes cats.
Can you house-sit a cat, and take her to stay with you? Also, it may not be fair to condemn her to daily antihistamines...but that is a decision for you. All the best in your decision. I realise this is just our experience though, yours may be different.