(This is one article in a series offering tips for teaching online. The suggestions and ideas shared are based solely on my personal experience teaching online for many years, and not on any "hard" research.)
I apologize in advance for this post. It is somewhat cynical and paranoid, and you may even think the recommendation is unnecessary and overkill, but when teaching online DOCUMENT EVERYTHING! And I mean EVERYTHING.
I have found the best way in dealing with these students is to respond quickly to their allegations with documented evidence refuting their claim (see, I told you this would sound cynical!). You must do all that you can to protect yourself from false allegations that may be escalated to your supervisor(s).
It begins with developing and publishing highly detailed course documents - syllabus, course schedule, assignments, etc. The more detailed these documents are - and provided you specifically instructed students to read the documents, and that they are accountable for ALL of the information contained in those documents (yes, you should be explicit in stating that students are to read the documents!) - you can offer a quick rejoinder of where information is located ("In the syllabus under the ASSESSMENT section, the second paragraph clearly reads, 'No Late Work Will Be Accepted.'"). Your position is bolstered if you also can indicate when these documents were available for review by students (e.g. "The syllabus was emailed to all students on [date], and was accessible on the course Learning Management System site three days before the start of class..."). Even better, some LMSs can indicate when a student accessed specific course materials ("...and you accessed the course syllabus on [date]."). So, be very explicit in both the content of your documents, and your instructions to students in how to use the documents.
All communication with students should be documented, including "announcement" posts, email messages, online chats, and video calls. Do not delete any announcement postings. These often contain critical information for which students are responsible, and usually have some sort of time/date stamp on the posting. As mentioned above, be clear with your students that they are responsible for all of the information posted in announcements (this may be an issue for some students who do not login everyday. Nonetheless, if the expectation is that all students are responsible for the information posted, then you are in a better position to address any "extenuating circumstances" individually).
"Carbon copy" (CC:) to yourself all emails that you send to students. I copy all student email communication to a separate email account that gets assigned to a specific class folder. Then, if I need to find a specific email, I can simply search within that folder. I recommend not "Blind carbon copying" (BCC:) email messages to students, simply because I want them to see (if they are interested), that I have retained a copy of the email thread (yes, I have had to print out entire conversation threads for administrators).
Following an online chat, I copy/paste the text of the entire conversation into an email, or a separate document, then share that conversation with the student, while keeping a copy for myself. This provides the student a record of what was shared in the conversation that they can then use in the future should they encounter a similar situation, but also provides you a record of the conversation. So, this can serve as a resource for students and an artifact for you, should you need it. Similarly, video chats can be recorded. Screencast-o-matic provides an easy, inexpensive way of recording your computer screen (Free for a limited recording duration). This video then can be shared with the student, and kept as future resource. If nothing else, audio record your video conversations (using Audacity or alternate sound recording program).
Finally, for every assignment a student submits, make a copy. Depending on how the assignments are crafted, and given the asynchronous nature of many online assignments, some students may attempt to "change" their assignment after submission, or claim that they never submitted the assignment because they didn't know about it. Depending on how you might use the copied document (e.g., are you going to make comments on your copy of the document or the student's original submission?), you might be able to simply take a screenshot of the document, and save the image file, or paste multiple image files into a single document. This works well for exam responses, too. Simply create image files of student responses for exam item responses or Gradebook entries.
Keep these files at least a year, but perhaps even longer (I suggest up to 4 years). I did have a student who went to the administration 3 years after having taken a course I taught (as she neared graduation) asking for the course to be dropped (and a failing grade removed), claiming she never got started in the course and just forgot to drop the course from her schedule. When I was asked by the administration whether she in fact did begin the course, I was able to produce documents that demonstrated the student did in fact work in the course, but stopped working a few weeks in based on the record of her accessing course documents, email communication threads, and gradebook screenshot images.
So, while far and away most students make every effort to work diligently and responsibly in your online course, you may encounter the occasional student who alleges "unfair," "inequitable," or "biased" instructional practices, or simply make claims that "they didn't know." By carefully crafting detailed and explicit course documents and instructions to students, and by documenting ALL interactions with students, you can build an evidentiary case that may protect you against such allegations and against student claims of ignorance of course policies and procedures.