I can certainly sympathize with your frustrations about support at LP. I too have had a couple extended run-ins with them, although not quite of the seriousness you experienced. I get the feeling that their first-line support has been offshored to Mumbai or something (please don't take offense, Mr. Patel -- most of the names are Indian, so that's my conclusion) and they're insufficiently trained and just working off scripts. For very routine work they're probably OK, but they're quickly in over their heads.
In this specific case, it sounds like LP is routinely scanning for possible malware (as well as back levels of applications) and got a false positive on your Wordpress installation. I would assume that there is a whitelist of known safe base64 usages to avoid flagging, but this one somehow got by. Was this a very recent WP update (not yet in their list), or code you had modified (and didn't match their template), or even very old code (that they didn't realize was still in use)? I would hope that they would be automatically alerted to multiple hits of the same occurrence, so they can quickly check that it's legit and can add it to the whitelist, and rescan blocked accounts. Maybe not. Let's hope their procedures get updated with every unpleasantness like this, so the same thing doesn't happen over and over, and customers are minimally inconvenienced. For starters, supply the code they flagged in an email, rather than having the customer have to guess. It's not a bad thing that they're looking around for malware, but it's not being handled correctly when they think they've found some. Certainly, blocking control panel access isn't good.
The moral of the story is: "Don't hesitate to quickly escalate to a supervisor if you feel like you're getting the runaround." The supervisors seem to be pretty competent and can usually fix things quickly. There just aren't enough of them to take care of first-line support duties.
You might want to post something in Review and Feedback, which has a better chance of Management seeing it (supposedly they read that area).