@yani and @mackieinva
Hi there, I looked through the whole problem again, and I have managed to eliminate the alternate wp cron tags.
As I have written, and so did mackieinva, I had no alternate wp cron defined in my wp-config file (or in any of the files for that matter). So I decided to add the define to the file. Of course, nothing happened. Then I simply changed the value from true to false, and ta da, the ugly tags disappeared.
So anyone getting the same results without a trace of the ALTERNATE_WP_CRON defined: you will need to add a new define line to the rest of your defines. Copy this under the many other defines in your wp config file:
save and check your site if it works. It works, hurray! :) (I have no clue about php, so it was a real trial and error treat)