Had to grab my copy of this book to answer this one! There are plenty of conversations between Allie and her parents (in that they have a very healthy relationship), but there is only ONE that Allie overhears. Allie overhears her parents discussing whether she should "see someone" about her "active imagination" such as words appearing in a mysterious journal and a calm voice helping her down from a steep cliff.
How do we know the conversation is overheard, as opposed to just a part of the story? Consider this part:
Allie got up and headed down the hall to the bathroom. She heard the murmur of her parents' voices as she passed their bedroom. On her way back to bed, she heard her won name and stopped to listen.
It is the dialogue between her parents during which Allie keeps silent and listens "expectantly." She hears them talking about Allie needing to "see someone."
"Like a counselor."
"Or a psychologist."
"Do you think it would help?"
"I don't know. I don't even know if it's really a problem. She's always had an active imagination. It's not something I want to discourage, exactly. It's just that I hate to see her lose friends over it."
"So do I. And I worry sometimes that she doesn't know the difference between what's real and what isn't. The thing about the words appearing in her journal, ..."
As the reader already understands, due to Allie's levelheadedness, psychiatric help isn't necessary in this case. This is just a case of two concerned parents speaking with each other about how to handle Allie's imagination and how Allie's imagination seems to be affecting her friends.
There is actually the literary quality of dramatic irony here. Dramatic irony is when we know something the characters don't know. We know, as readers, that Allie really DID hear a voice that helped her down from a steep cliff and that she DID see writing in the journal that wasn't there before.
What is her parent's decision? Easy. "Let's give it a while, ... [and] keep a careful eye on her." It is wonderful to see such concerned parents even though the parents, who are always logical, think that Allie is exaggerating.