Let's say one player has the Healing skill. The other player wants to assist but is without that skill, however she has skill Knowledge: Biology. Would it be within the rules to allow her to make a cooperative check to help out?
The rules specify that you cannot assist with a cooperative roll unless you are trained in the same skill. So, by RAW you cannot assist in the situation you describe.
However, I can envisage circumstances where this might be allowable at the GM's discretion, if and only if it makes sense within the fiction and characters background. This is going to depend massively on the genre/setting, and the skill sets of the characters you have in the group. Using your example, for me it would depend on exactly what background the character with Knowledge(Biology) has as to whether the skill might be applicable or not.
If you start allowing this kind of thing regularly then you are effectively allowing skills to be much broader than they are as written. This may or may not be a good thing. Skills with particularly narrow and specific applications such as Healing would start to lose their 'niche' as well.
At the end of the day, despite the RAW there is certainly a case for allowing it, but you will need to think carefully as to how often, and make sure that it makes sense within the fiction and doesn't impact the way skills work within the campaign/setting.
The rules, as written, aren't explicit. They do say:
… which strongly implies that a character must have the actual skill being used and can't substitute another one. A very liberal reading of the rules could take that to mean that, for example, "When helping someone with Healing by using theoretical knowledge, Knowledge: Biology is the skill in question".
That said, it seems reasonable to house rule this as OK and I would allow it in my games in some circumstances (in particular those where advanced theoretical knowledge would be more likely to help, such as treating a new disease rather than basic first aid).