It is true, if you're HPV negative your sample will not be checked further.
I suppose the reasoning behind it is a tricky thing to discuss without causing upset. All screening programmes miss cases of the disease they're screening for. With cytology based cervical screening, it could be human error reading the slide, or operator error taking the sample, or just that the sample came from an area of the cervix with no abnormal cells, although there were some on another part.
With HPV based screening it will be that a small proportion of cancers are not HPV related (there seems to be some dispute about how big that proportion is, I've seen a range from 1 to 11%). The NHS has made the calculation that screening will catch more cases if it's based on HPV than cytology. But nobody really wants to say "yep, sorry, we will potentially miss your cancer if it's not HPV related, but we will pick up someone else's that would have been missed in cytology." Inevitably it's also to do with money and staffing - you could argue the best option would be HPV testing and cytology, but the NHS can't afford that.
The good news is at least that research shows that the HPV vaccine is making an appreciable difference to the number of cases developing, so that's something.