^All the characters are owned by Marvel. Other studios just hold licenses to make movies about them. That's more like leasing than owning.
As I've said, I'd like to see Sony and Marvel Studios find a way to at least loosely integrate the Garfield Spidey films with the MCU. It's a new enough continuity that it would be easy enough to keep them compatible. I do think the X-Men films and the whole mutant continuity work better as a separate entity, but I agree, Spidey would fit in just fine. I doubt we'll ever see Andrew Garfield teaming up with Downey, Hemsworth, and Evans in an Avengers movie, but there could be some subtle cross-references and an effort to keep the series broadly compatible. Say, have a lot of construction going on in the background of ASM2 because Manhattan's being rebuilt from the Battle of New York.
Of course, that wouldn't necessarily benefit Agents of SHIELD, since they probably wouldn't get to feature any Spidey characters or continuity that hadn't already been introduced in the movies, so as not to restrict the moviemakers' options. And with Spidey movies coming out so infrequently by comparison, there wouldn't be many opportunities to do any kind of tie-in. Heck, that's the whole reason to do a series about a new cast that stands largely apart from the movies -- it's just better from a logistical standpoint if a TV series isn't too closely tied to an ongoing, much more slowly developing film series. So any Avengerverse/Spidey crossover elements would be far more likely to show up on the big screen than on TV.