No, not true at least in my opinion.
When a girl proposes, if the guy has the same feeling for her, then it would be no less than a dream for him. I think it will enhance their bonding because they preserve something which is not very common and always makes their relationship special and unique.
In the opposite case, if a girl proposes a boy, who lacks the feeling for her, this might cause little trouble for her (mentally), and of course, depends on the guy how he reacts to this matter. If the guy is mature enough, he will understand the matter and would definitely respect her feelings.
The first thing is girls do not propose because they feel shy and are more sensitive compared to boys. Also as per the culture going on in our society, when a guy proposes a girl, she has the privilege to say either yes or no, and boys take it light compared to girls. But when a girl proposes the guy, and if the response is "NO", it hurts her badly and scratches her self-esteem and confidence as well.
I feel it totally depends on the guy. Supporting the fact that “boys propose girls” is common and adapted by the society, pretty well but there are lots of couples and relationships, in which the girl has initiated and proposed to her partner, continued and living a happy life.