I agree with you that immigration do liaise with the Revenue Department, though in your case, you're referring to an extension of stay based on employment, where evidence of tax being paid is a valid request. For those of us who are retired there has been no requirement to show any tax paperwork when doing an extension. However, should the RD have some concerns about your tax status here as a retiree (or even just pick you at random for an audit), they can, and will, flag your passport so it comes up on the immigration computer. The onus is then on you to get that flag removed before you are allowed to leave the country, and, in theory, even get an extension. As I have posted here on other threads, this happened to me when they decided to audit my taxes. Luckily my local immigration saw the catch 22 between not giving me an extension and not allowing me to leave the country, so did extend my permission to stay while I sorted it out. They could have just given me a short term extension while I sorted it out, but gave the full year. From what I've heard, other offices are not as lenient.
There was no problem with my taxes. I was doing the valid, at the time, not transferring money until the year after it was earned tactic, however, trying to find out the exact tax office responsible took some time - it was a Bangkok one, not my home province, and then even when they were satisfied, the flag remained. I had to visit the immigration office in Soi Suan Plu, where the black lists are controlled, to do so. That part was simple though. Once I'd found the right office I explained what had happened and the woman got on her computer and removed it there and then.