There are occasions in FSN where they say "Servant" but mean "Heroic Spirit." It's like how when, in narrative descriptions, you might call Rin a witch, even though she is not a Witch. Just like how sometimes they call Saber a Heroic Spirit, when we know, actually, she isn't one.
What does laying eyes on an anti-hero even have to do with this?Heroic Spirit is just a blanket term for everything summoned from the Throne. I've seen the translation called into question. Anti-heroes are Eiyuu, doesn't mean they fall under "hero" when being compared to Achilles. Especially since he never laid eyes on an anti-hero while alive as far as I know.
The actual Noble Phantasm is a conceptual representation. With it, he may in fact actually be faster than he was in life. Or even slower. But the idea is that he's going to be bumped to beyond any other.
Probably similar to how Gil, despite not actually necessarily owning the origin of all heroic legends in life, is obliged to have the origin of all heroic legends.
Cu Chulainn can, say, arrange flowers beyond the level of a regular human. Does that make his flower arrangements Servant level? How do you even define Servant level from not-Servant level? That's sort of the point Canon is making. "Servant level" is ill-defined and may be completely pointless when narrowing down things that really have no metric and things really unrelated to actual human limitations.That's fair, but I think Servant level would be the implication considering he's, you know, a Servant.