Rules Question: Eldritch Heritage + Bloodrager

[Minigiant]

A very quick question

Can a Bloodrager take Eldritch Heritage, and select a Sorcerer Bloodline of the same name as the Bloodrager one they have?

or asked like this

Can an Arcane Bloodrager select the Arcane SorcerermBloodline through Eldritch Heritage?

[MrCharisma]

I'm gonna say no, but I'm not an expert =P

[Firebug]

Eldritch Heritage, specifically "Benefit: Select one sorcerer bloodline. ... This bloodline cannot be a bloodline you already have."

The bloodline ability of Bloodrager ends with "If the bloodrager takes levels in another class that grants a bloodline, the bloodlines must be the same type, even if that means that the bloodline of one of the classes must change. Subject to GM discretion, the bloodrager can change his former bloodline to make them conform." The text of which is mimicked in Eldritch Scion/Blood Archanist/etc.
Basically its the same bloodline, "Arcane", its expression is just different depending on which class you have mechanically. I was certain there was a clarification somewhere, but it might have been a PFS ruling.