As I said earlier, this is the oversight in the rules.If you want to argue RAW:
The codex entry states that the Herald's unit type changes from Infantry to Jetbike, and the rulebook states that the +1 Toughness is granted to bike riders:
"Bike riders benefit from the protection offered by their bike, ...". (Emphasis added.)
Compare the description of the chariot:
"... and changes [the herald's] unit type from Infantry to Jetbike." (Pronoun substitution and emphasis added.)
The RAW argument fails because the rules don't specify either a) that the chariot is a bike or a jetbike (so that the herald is a bike rider) or b) state that the herald is riding a bike. Instead, the Herald is simply a Jetbike as per the unit type designation, and follows all of the rules specified for Jetbikes.
Summary: Heralds on Chariots of Tzeentch are Jetbike models who are not riding bikes, so therefore do not get an additional +1 toughness for being Bike riders.
That is a very poorly written passage, it doesn't really provide you with the specific information you need to play the rule with any certainty about what it means.
Since it's under the unit type, and makes no reference to wargear, or excluding models which don't actually 'ride' their bike, it's safe to assume that it's just a stupid way of saying "Bikes get +1T".
If you want to pull that, then an examples should be brought up.
The Turbo Boosters USR states that "Any model mounted on a bike" may boost; ok then, what you're saying is that Necron Destroyers and Scarabs can't Turbo Boost, because they aren't MOUNTED on a bike.
What you've done is mixed fluff with rules, and unfortunately the rule did that; it's a stupid mistake made by GW, I'm sure they intended it to mean any Bike unit, not Bike rider.
Anyway, I'd say that the Herald is, in fact, riding a bike, thankyou very much.
And your summary is ridiculous, once again mixing rules and fluff to make an absurd conclusion; he either is or he isn't, there's no halfway point.