Should I include these files or not?
Dees answer was "suggest edited" to be more readable but was rejected (do not understand why- new user here) See here is screen shot of a slightly edited Dee's answer
I think Dee's answer gives examples of what is safe and dangerous as well as why. After giving examples of situations of what is and what is not safe or dangerous and then answers "it is up to you"; that is after you take those examples he just listed (as well as qbi's answer) into consideration.
What is "dangerous" about someone else knowing my computer's hostname?
Nothing if that person is trusted and trustworthy.
For example the person using a knife to chop vegetables could be described as safe(trusted and trustworthy) but the same knife could be used to cause a fatal injury. It just depends who is using the knife. The knife itself is just a tool. So to make it all relative think of the knife as the host name. Hostname is essential for clients to speak to hosts (how internet works)- just like it is essential to chop or peel vegetables before you cook or eat them.
Regarding the warning about the possibility of sending sensitive information qbi illustrates in their answer how the accumulative information in the example given of how a hostname could reveal workplace/employer information. So that could be described as being sensitive information for many different reasons. Use your imagination.
The warning box is showing Ubuntu developers respect your privacy and are asking permission for information which may be useful for making Ubuntu even better.. That is after informing you that other information relevant to problem that could be described as personal or sensitive information may be contained in the logs being sent after your approval and therefore consideration may have to be taken according to circumstances/situation before sending logs.
There is no definitive answer to the question being asked as each time a request is being made it is probably due to new logs being made because of an error or problem being detected and these logs will be different according to the problem in the first place. A decision has to be made each time if you wish. Just say no each time if that is easier or cancel sending report all together; if you think that is appropriate/helpful to you. When sending error reports; you are only helping developers to evaluate the problem detected so that they can prevent, cure or remedy the problem which is likely to help more people than just yourself in the long run.
Eliah Kagan's and Private's comments to your question more than help to get realistic perspective.
N.B. Am not bounty hunting here as i think the contributions allready made have answered your question and the bounty should be split between qbi's and Dee's answers but that is up to you. Some rep would be nice though! :)