Sorry for the long response - I'm by no means a legal expert on this, can only see it from how it has worked for me in the past....
It depends on the quality of the applications received. If you get 1000s of applicants that are equal to the applicant you are trying to hire, then it would be more difficult. But it really depends how thorough your recruitment processes are - if you don't record basic details (like scores or reasons for rejecting) it can be more difficult. The main way you prove your ability to obtain a tier 2 though is to show you have advertised the role throughly. Most firms have to get letters from at least 3 universities to confirm campus activity, plus show their website + other job board advertising to show the role has been widely marketed.
The only difference between those who have a gap in their tier 4 to tier 2 is that they are part of a national quota for tier 2s. Those who move directly from tier 4 to tier 2 are not part of the quota. The process is identical though, the only other difference is that the person with a gap would have to return home to obtain their tier 2.
As far as I am aware the quota was only hit this time last year and they thought that was due to the high amounts of graduate programmes starting in September (
http://www.workpermit.com/news/2015-06-20/uk-tier-2-visa-limit-reached-for-first-time). However even then, some firms applied again the following month when the new quota was available and still managed to get their visas in time. The monthly quota rolls over if it isn't used which has meant 99% of the time it's been an easy process to obtain a tier 2 (as long as you meet the basic criteria).
Based on this, a firm's theory that they cannot get a visa for someone if they are not directly transferring from another visa type is questionable. Maybe they just saw it as too risky somehow...
Like most organisations, an employment contract would state that any offer is subject to you obtaining the right to work in the UK. I guess firms might be concerned about losing a recruit weeks before a start date (firms with small intakes will be more worried about that), or the potential loss of money of training someone (LPC fees etc) who can't then start. They might not also want to additional costs of the candidate flying back to their home country (a lot of firms don't cover those costs anyway though and make it clear the candidate will have to cover it).
So to me any of those perceived risks are fairly minimal, especially where the quota has only been reached once in roughly 5 years.
But even if it did happen, my thought would be that as a firm you'd just reapply for the tier 2 and at worse move the person to the next trainee intake. That's what I have done before when there have been delays in the work permit process. The only way you wouldn't be able to do that is if you didn't meet the criteria for the work permit, but then that would be the same case if you were moving directly from a tier 4.
So I suspect the whole truth is not being explained by the firm in question.
They either haven't got a certificate of sponsorship in place (feasible but then they couldn't recruit any other non-EU person into any kind of role unless it was someone who already worked at the firm).
Or it is possible that their selection processes/recording of them are not robust enough to obtain the visa.
Or that the role does not meet the tier 2 criteria, which is usually only down to pay.
Or they are concerned about the additional risk + potential costs of someone being on the quota system.
But to say it is because of the tier 2 process because of an "exemption" is not quite accurate in my eyes. With the exception of the final reason (which to me is pretty weak anyway), the same would apply if you were transferring directly from a tier 4 to a tier 2. Unless things have changed recently that I am not aware of!
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