I'd ask them why they recommend a 10w30 vice a 5w30 and see how much they know.
The first number in the rating, e.g. 5w or 10w is the oils weight when "cold". This viscosity is normally measured at 40C, or 104F, so it isn't really "cold". The second number, e.g. 30, is the oils weight when "hot". This viscosity is normally measured at 100C, or 212F, very near the normal operating temp of the oil.
Both 5w30 and 10w30 are 30 weight oils when warmed up, so essentially they are the same. Many people incorrectly read the weight classification when cold and think the oil is less viscous due to the lower number. But, the rating system is different at 40C than at 100C. A 5w viscosity at 40C is about six times higher than a 30 weight at 100C. For example, Mobil 1 5w30 viscosity at 40C is 64.8 cSt, and at 100C is 11.3 cSt. Switching to a 10w30 will result in an even thicker oil at startup, robbing HP, fuel economy, etc, and will provide little to no benefit when hot.
Viscosity Improvers are viscous chemical compounds called polymers or polymeric compounds that decrease the rate at which oils change viscosity with temperature. These viscosity modifiers extend a motor oil’s operating temperature range and make multigrade or all-season oils possible. The VI is measured by comparing the viscosity of the oil at 40°C (104°F) with its viscosity at 100°C (212°F). VI can provide insight into an oil’s ability to perform at high and low temperatures. Petroleum-based motor oils require the use of viscosity improvers to meet the low temperature requirements of SAE 0W, 5W or 10W and the high temperature requirements of SAE 30 or heavier oil. Synthetic-based motor oils have a naturally high viscosity index and require less viscosity improver additive than petroleum oils.
Given this, for a good synthetic, there is little benefit to running a 10w30. But... it probably won't hurt either.