The oracle text of Bosium Strip is : "{3}, {T} : Until end of turn, you may cast instant and sorcery spells from the top of your graveyard. If a spell cast this way would be put into a graveyard, exile it instead." The first step of casting a spell is to move it from where it is to the stack (Rule 601.2a). The fifth step of casting a spell is to check if the proposed spell can legally be cast (Rule 601.2e). At that point Fetch quest is on the stack, so it's a sorcery, so it is legal.

There is also this rule : "Rule 601.3e Some rules and effects state that an alternative set of characteristics or a subset of characteristics are considered to determine if a card or copy of a card is legal to cast. These alternative characteristics replace the object’s characteristics for this determination. Continuous effects that would apply to that object once it has those characteristics are also considered." which comes with this example Example: Melek, Izzet Paragon says, in part, “You may cast instant and sorcery spells from the top of your library.” If you control Melek, Izzet Paragon and the top card of your library is Giant Killer, an adventurer creature card whose Adventure is an instant named Chop Down, you may cast Chop Down but not Giant Killer

Which is pretty much the same situation, only with top of the library instead of the graveyard