Your question title asks whether you "can" be fired. Barring specific circumstances, such the firing being based on you being in a protected class, your employer "can" fire you for any reason they want. But you seem to be asking a different question, namely whether your firing is for-cause for Unemployment Insurance purposes.
Assuming you are otherwise eligible for UI, one of your first steps should be simply asking your formal employer whether they intend on asserting to the EDD [Employment Development Division, for non-Californians] that you were fired for cause, or otherwise disputing your UI claim.
As for the passage you quote:
In situations involving preemployment activity, the claimant is discharged for conduct occurring before the employment relationship was begun.
In other words, "involving preemployment activity" is defined as being based on conduct occurring before your employment relationship began. I'm not sure what "employment relationship" includes. It definitely includes any time you were employed, and may include activity during the recruitment process, such as interviewing and submitting a resume.
Usually this is not connected with the most recent work.
Situations involving preemployment activity are generally classified as "not connected with". The passage makes reference to Title 22, Section 1256-33(c)(1), which states:
This section interprets when a discharge for misconduct is or is not “connected with” the most recent work under Section 1256 of the code.
In other words, this section talks about how to tell whether something is "connected with" the most recent work; this section gives the reader an idea of what "connected with" means.
Misconduct is connected with work if the activity involved injuries or tends to injure the employer's interests.
To be "connected with" work, an act has to affect, or have the potential to affect, the employer.
A claimant who has been discharged from work for misconduct is disqualified under Section 1256 of the code only if the misconduct is “connected with” his or her most recent work (see Section 1256.3 of the code and Section 1256-2 of these regulations for definition of most recent work).
Whether something is "connected with" the most recent work is important, because any misconduct that is not "connected with" the most recent work is not a basis for disqualifying you from UI benefits.
Title 22, Section 1256-33(c) also says "If there is no injury or potential injury to the employer's interests, the employer cannot reasonably impose the employer's standards of behavior on an employee during his or her off-duty time." It is reasonable to interpret this as applying to pre-employment activity as well. So if what you did caused no injury to your employer, then it does not keep you from collected UI benefits.