Is it true that girls tend to be attracted to the guys that give them the least amount of attention?

Not in exact sense.

Girls are humans but certain characteristics are inbuilt in them. Ironically they will fiercely deny it if you ever ask them.

Girls like independent Alpha males. What does an Alpha male do? He is busy in his goal, life, business, job or whatever. He has a single point focus on his motive in life. He has bigger goals. Naturally he would give his girlfriend less attention and less time. It inadvertent and not planned.
Women will ever tell you to love them more, follow them and give them infinite praises and attention. If you really start doing this, they will screw you! This is the contrast between what women think and what women really do. Its inbuilt into them. We have no control over our instincts. Whenever men see a sexy girl they want to fuck her (in mind). There is no way to stop that. We may publicly say and even behave in decent manner but we cannot suppress our native instinctual desire. Yes we will curb it to follow social norm but desire will stay. Similarly what women say or think is programmed into her conscious mind by media and society. But what she instinctively feel is altogether different ball game. So many guys fail to understand this subtle difference in two brains in any woman. The physical rational brain and the emotional biological evolutionary brain. Men also have biological brain but usually for free sex.
A normal man is not that much busy in his regular life. The greatest mistake guys do in relationships is that they follow too much, give too much attention and eventually these bored girls leave them. Remember a girl always wants someone better than her.