Yes, you can gain a familiar elsewhere and have both
This ambiguity is due to a very annoying habit that Wizards of the Coast had to assume that all characters were starting from 1st-level, would remain single-classed, and would not take cross-class skills, when discussing what members of a class can do. You see this in similar issues like:
In all three cases, the text states restrictions in very broad, unqualified terms, but the restrictions only make sense if you assume a single-classed character with only in-class skills. They also, of course, ignore even the possibility of future content changing things.
This was probably to try to make things easier to understand as a new player, by not bringing up various potential other considerations that could come up, but it makes it very difficult to draw the line here. The consistent response (validated, in some cases, by future books, errata, or developer commentary) has been
These kinds of restrictions about what members of a class cannot do only refer to what that class is letting them do, not imposing a restriction on what other classes, skills, or feats might allow.
So the necromancer loses the Summon Familiar class feature of the wizard class. He could still gain a familiar from, e.g., taking levels in sorcerer, or the Obtain Familiar feat.