No, white clothing does reflect more heat than black clothing. However the answer to which is better to wear in hot weather is "it's complicated", the TL;DR is that for tight clothes white is better, for loose clothing black and white are the same.

So the fit of the clothing is actually more important than the colour. However, if you are going to be wearing tight-fitting clothing, then stick with white. Fabrics with texture – such as seersucker or pique, a fabric often used in sports polo shirts – also help to lift clothing off your skin, rather than staying snug and tight-fitting.

Light gets converted into heat, white rejects more light before it can do that.

Colors work by which parts of the light spectrum get absorbed and which get reflected. A shirt that absorbs most wavelengths, but largely reflects green, will look green.

And in that same vein, colors will appear darker, if less light is reflected in general. So, a white shirt may reflect 90+% of light, whereas a black shirt may absorb 90+% of light.

And ultimately, absorption means that the light's energy is turned into warmth. So yeah, a darker shirt heats up more in the sun.