I know that you said Europe rather than the middle east, but I currently have a book out by a 12th century Syrian author named Usamah ibn Munqidh, and I thought, as it has a lot about falconry from a noble perspective, and is from your time period, that you might be interested if I reproduced a bit of it here (it's a translation by Paul M. Cobb).

Basically in medieval Syria and Egypt it was more or less like you guessed, the nobles would watch while their falconers flew the birds. In fact in one of his stories Usamah mentions that Nur al-Din offers him a goshawk, as he is known to be really into hunting, but he turns it down explaining that: 'we don't do our training ourselves. We have austringers and attendants who do that and who go ahead of us with them to hunt.'

Usama describes hunting at the court of a number of people (he was exiled from home, and spent most of his life at the courts of various middle eastern rulers), and goes into a bit of detail about how Zangi hunts with falcons. It seems rather lavish, but the basics are quite similar to most of his other stories:

I have observed the hunt with the King of Amirs, the atabeg Zangi (may God have mercy upon him), who had a large number of birds of prey. I would see him, as we proceeded along the river-banks, preceded by the austringers, who would cast off the goshawks at the waterfowl. the drums would be beaten following the usual custom and the hawks would hunt down what they could hunt, and miss what they missed. Behind them were the 'mountain' peregrines on the falconers' fists. Once the goshawks had done their hunting (successful or not) they slipped the peregrines on those birds which had managed to fly far away, making a 'desert run' [the translators notes explain the reading is uncertain, he presumes that it's a Persian technical term involving the desert; an earlier translator went for 'and had perched on an elevated place'], and they would take them and make a kill.

I don't know quite how this compares to European falconry of the period (it seems a lot larger-scale and more organised than anything I've read) and Usamah only has one story involving European falconers. He was hunting with King Fulk of Jerusalem, where they met a Genoese man who had a dog and a goshawk which he had brought over from Italy (obviously he thought they were fairly important to bring them all that way). The hawk would hunt cranes, and the dog would run along underneath, and then catch the crane when it was brought down to earth. The Genoese man told them that in his country if a hawk has 13 tail-feathers, like his one, then it could hunt cranes (the notes explain that birds of prey have 12, so he was either having them on, or perhaps meant that it was very rare).

He does mention some nobles that put a fair bit of time into their birds though, in particular he's got quite a long story about a hawk of his father's named 'al-Yahshur'. Al-Yahshur was a hawk from Cilician Armenia (it's now south-eastern Turkey) who was 'so broad in the chest it looked like a falcon'. It was initially trained by Ghana'im, their austringer, but it seems to have pretty much been his father's pet after that.

Al-Yahshur's roost was with my father (may God have mercy upon him), who would not leave it in the care of the austringer because the latter would always carry the hawk around at night and starve it to get better hunting out of it. But al-Yahshur would see to its own needs and still do whatever was asked of it.

He then explains how his father hunted with it.

[when they found a partridge] he would say, 'Give me al-Yashur!'

The moment my father would raise his arm, al Yahshur would fly from the wrist of the austringer and perch on my father's wrist, without any other call... upon nearing the sleeping partridge my father would throw a stick that he was holding, flushing it. Al Yahshur would now be slipped on the partridge, which it could seize anywhere within a range of ten cubits.

He then continues about how his father would only let it catch five or six partridges, so as not to strain it, and then he would gorge it, but it would still hunt a few partridges on the way home (out of duty, because it was a family-member apparently), and then when they got home he'd give it water for a bath, and put its perch by his bed. There was a bit more about it, like how you could have it in a courtyard with pigeons and ducks, and it would ignore them, and then when it died a neighbouring lord, who used to borrow it sometimes, gave it a big funeral. I'm not entirely sure how reliable this is (for one thing it all happened about sixty years before the book was written), but it does seem like this guy, while he may not have done the initial training, flew the hawk himself mostly, and looked after it too.

EDIT: One more story: 'Once we had left the town, the falconer would let two peregrines circle around, and they would continue to circle above the hunting-party. If one of them should strike out on its own, the falconer would merely cough and point with his hand in the direction in which he wanted the falcon to go. And, by God, the peregrine would instantly turn back in that direction.'

Could someone who knows about falconry tell me if that's at all possible? It doesn't seem very likely, but then I don't really know anything about falcons.