No. A 5W20 (for example) is a 20 weight oil, on the hot end, regardless if it is a dino oil, synthetic oil, a blended oil, or olive oil. A 20 weight oil is a 20 weight oil.
From what I've heard from some mechanics, they said on cold starts, synthetic is better because conventional oil gets like a little gel like at cold temperatures and doesn't get around as easily.
This is what the W means in 5W30 (since this was about sports)
W means winter or cold weather viscosity. So if you take a 5W30 and a 10W30, both will perform exactly the same at operating temperature, a 30 weight oil, only difference will be how they behave at cold start temps.
This is a pretty basic explanation, but should give you the gist of it. See the cSt numbers. So what you've been told is partially correct you could say, but not in terms of synthetic vs dino
MOTORCRAFT® 5W-30 PREMIUM SYNTHETIC BLEND MOTOR OIL
SAE Grade 5W-30
API Service GF-5/SN
Specific Gravity @ 60°F (15.6°C) 0.860
Density, lb/gal 7.17
Flash Point, COC, °C (°F) 206 (402)
Viscosity:
cSt @ 100°C 10.8
cSt @ 40°C 65
cP @ -30°C 6,300
Viscosity Index 163
Pour Point, °C (°F) <-42 (<-44)
MOTORCRAFT® 10W-30 SYNTHETIC BLEND MOTOR OIL
SAE Grade 10W-30
API Service GF-5/SN
Specific Gravity @ 60°F (15.6°C) 0.871
Density, lb/gal 7.25
Flash Point, COC, °C (°F) 224 (435)
Viscosity:
cSt @ 100°C 10.4
cSt @ 40°C 69
cP @ -30°C 5,900
Viscosity Index 157
Pour Point, °C (°F) <-42 (<-44)
Now here is Valvoline conventional (non synthetic oil)
http://www.valvoline.com/pdf/premium_conventional.pdf
or
Mobile 1, a grade 3 sythetic
http://www.mobiloil.com/USA-English/MotorOil/Oils/Mobil_1_5W-30.aspx#