Grey hair sprouting all over?
Well there is some truth to that because grey hair has a faster average growth rate compared to hair with pigment (on the same person - as opposed to the previous post where pigmented hair grew faster in younger women compared to post menopausal women).
This actually somewhat related to hair thickness because grey hair is on average thicker than hair on the same head that still has pigment. However, there are likely to be other additional factors (Eur J Dermatol, 14: 28–32, 2004).
More Care For Grey Hair?
Yes, grey hair needs much more care and it is purely related to the fact that it has no melanin (Journal of Cosmet Sci, pp 103-118, 2001). The sun affects grey hair much more than it does hair with pigment, this is because it degrades the amino acids that make up up the protein in hair and makes hair weaker (if you are keen on details the specific amino acid is tryptophan)
Some studies have shown that as little as 15 continuous days can create loss of 85% of this amino acid. Remember, sun damage is cumulative which means if you have half a day of sun shine today and half a day tomorrow, your hair has had one day of UV exposure. You cannot repair the damage from the previous half day.
What you can do is use sunblock on your hair (noting that hair products do not have regulation on sunblock though). You can also look for this ingredient - Cinnamidopropyltrimonium chloride aka CATC aka Incroquat UV-283 which is a UV absorber.