Can asking a girl to be your girlfriend actually be a turn-off?

I'm a 26M dating this 27F woman for a little over three months now. She's great and I'm definitely developing feelings for her, and we've both talked about it and agreed we're both looking for a long term partner.

After about a month I asked if she wanted to be exclusive, to which she replied she did really like me and want to head in that direction, but it takes her a while to open up and trust people for a relationship. I agreed, but clarified I was looking for exclusivity but not necessarily a relationship. She recognized the difference between the two after I explained but still didn't give a definitive answer (i.e. exclusivity yes, relationship no).

I was thinking of asking her again this week now that more time has passed, but I recently heard that it can actually be a turn-off to women when you ask them directly to be official (regardless of what they might say).

Has anyone observed any truth to this? I've already made it clear what I'm interested in, so maybe it would be better to let her bring it up at her own pace.

On the other hand, as much as I do like her, maybe it would be better not to be on the hook waiting around for her to bring it up only for things to fizzle out and waste my time should it turn out she never actually liked me that much. Figuring out for certain whether she likes me enough to commit at this point could be the better play.