Article 14(1) of the Treaty on European Union (PDF) states that the European Parliament "shall elect the President of the Commission". Digging deeper into the Treaty, the actual mechanism is that the European Council, acting by qualified majority and taking into account the results of the European elections, nominates a candidate, who the European Parliament can elect or reject (Article 17(7)). So Merkel's correct that the European Council isn't required by treaty law to nominate the winning party candidate, but that's not to say that a political convention of nominating the winning candidate cannot - or shouldn't - evolve. Just as it's now accepted in the British system that the Queen appoints the winning party leader Prime Minister (although it may get more complicated if coalitions start becoming a regular feature), it should become accepted practice for the European Council.
I can see why Angela Merkel has difficulties with this. The PES candidate is from across the political isle and would cost her the ability to nominate a friendly CDU/CSU candidate as a Commissioner, losing her power within the Commission and patronage within her own party. Other Member States may start to have difficulties with it as well, either simply because they don't like the winner or because they realise that their own power to nominate Commissioners could be undermined if a coalition is needed to elect the Commission and its president - a coalition that may include Commission portfolios as part of the deal...
It could be argued that this democratisation of the Commission leaves it too dependent and close to the European Parliament. Article 17(3) TEU states:
"In carrying out its responsibilities, the Commission shall be completely independent. Without prejudice to Article 18(2), the members of the Commission shall neither seek nor take instructions from any Government or other institution, body, office or entity. They shall refrain from any action incompatible with their duties or the performance of their tasks."
The nomination of Commissioners (that can be rejected by the Commission President) is the only exception to this independence rule. So the argument is that giving the Parliament such a big role would damage the Commission's independence.
But the Commission is already, by treaty, responsible to the European Parliament and can be voted out of office by it (Article 17(8) TEU). Despite the complicated nomination-and-election procedure, there is clearly a tendency towards political accountability to the Parliament and the electorate. The means are there to make the Commission more democratic, and the opportunity should be seized. The concerns over the "independence" of the Commission are therefore more a defense of the status quo than anything.
The principle that the Commission consists of representative of all (or a representative rotation) of the Union's nationalities is a kind of consociationalism - a way of making sure that all groups feel that they are represented. But why should the nominees to this office be so naturally assumed to have the political colour of the nominating Member State? Surely this ends up replicating the political balance of the Council, rather than the Parliament? It seems odd to stress the dangers to independence of the Commission from a Parliament that can hire and fire it, but not the political influence that comes from basically replicating a snapshot of the political balance of the Council in the Commission.
The Commission will always be sensitive to the political make up of the Council and Parliament, since it has to get their consent to pass legislation. Independence therefore should be seen more strictly, as concerning direct instructions from governments and outside bodies and propriety in office, rather than independence from the Parliament and the electorate. Political accountability matters, and we need more of it in the EU - so come the election the new Parliament should make a stand on the issue of who the European Council nominates. It should be the winning candidate.