Just popping on to say this is absolutely correct. The people who think that no solicitor would ever encourage or assist someone to pursue an obviously futile claim are sadly naive and mistaken. Yes there are ethical codes meaning they can't actively mislead the court or lie to their client but there's a very big margin between that and writing some letters or submitting a claim that may not be strictly arguable or have a very low chance of success. And the same goes for the happy assumption that if OP is clearly on the right side of the law (according to MN verdict anyway) she can simply either take the law into her own hands and assert her rights by booting the man out of the house, sending him a bill for rent and/or that the court will swiftly and efficiently strike out the misconceived or vexatious claim without OP having to shell out for her own solicitors and legal advice - I wouldn't want to live in the world where the former is true i.e. people are allowed to act first and legally prove they were correct later, if the latter was true it would be great but that would require a well resourced and efficient modern lower tier court and tribunal system which tax payers seemingly are in no way prepared to fund...
I work in the HR/employment law field and it's incredibly common to receive letters and/or ET1 claims from solicitors for things that are totally and obviously misplaced/misconceived (e.g. unfair dismissal claims when the person doesn't have the requisite service), badly drafted (often obviously with the dubious assistance of ChatGPT), lacking particulars or vital information - just rubbish that isn't worth the paper really. But that doesn't absolve the employer of the requirement to respond and answer the case all the way through the various tiers of the court if necessary, all of which costs time, money and stress, no matter how clear cut the victory at the end is (and before you ask no it usually isn't possible to recover costs from the losing party no matter how badly they ran their case).
The solicitors that engage in this kind of thing tend to fall into two camps, one is the 'shark' firms who will happily charge a client a couple of hundred quid to send any old rambling toilet paper of a threatening letter to their (former) employer without bothering to advise them properly as to their actual prospects, sometimes this will spook the employer into coughing up a bit of cash, sometimes not but they still get paid by their client either way. Or, in some ways more dangerous, the 'a little knowledge is a dangerous thing' brigade, the friend of a friend or second cousin who took a law degree a decade ago or who practices in a totally different area of the law, who will aid and abet the aggrieved complainant all the way through a lengthy and ultimately futile process with bad advice and poor quality submissions - dangerous because while the sharks can usually be put off by either a robust and aggressive rebuttal or shelling out a modest sum to make them go away, the passionately misinformed party usually wants (perceived) justice to be done and won't settle for less than what they believe to be their full due, however unlikely that is to be delivered by the law... I wouldn't be surprised if the OP's chap and his solicitor are one of these and there's really nothing to be done but pay up for some good legal advice and then wait for the sloooowww machinery of the law to turn and do it's thing...