It means, what it means. By 'fawning over your needs', that sounds like it should be read in the context of 'caring for a pet or small child'. Like food, water, shelter, cleaning.
You can order them around, that doesn't mean they're going to listen to you. The creature will attempt to protect and care for you. It does not mean it will listen to you. Yes, it will (possibly) take into consideration your words, if they match up with what it desires and believes (which is that it wants to watch over you fawningly and adore you, and hug you and squeeze you all to bits).
For instance, an ogre will want to keep you around, probably set you in a cave, and it will likely drop hunks of uncooked meat and smelly furs near you to feed you. You can say you're a vegetarian (and it will probably uproot a bush) but you can't tell it to take you to town.
If you were sick (obviously enough that it could tell), it might try some of its own (probably repulsive) ogre remedies; smearing you with animal grease, rolling you in dung, etc. If you somehow did convince it you needed a cleric or a doctor... it is probably more likely to go and kidnap one than take you to town or the temple.
You can't be like "I neeeed to have 1,000 gold pieces to buy a new sword" and expect to be given 1,000 gold pieces or even a sword. Those aren't the needs at hand, think of yourself like suddenly being a frog in a jar to the target. You need air holes in the lid, you need bugs, and "you need a stick and a leaf... so you think you're in your natural environment."