Cash out refinance lending question

[David Hess]

I have got some conflicting information about whether we can do a cash out refinance in our situation and am seeking clarification.
Here are the details.

Our primary residence is in San Jose, Santa Clara County were the conventional/jumbo line is $767,500.
. Recently appraised for $1,150,000
. Primary mortgage remaining balance $426,466
. Home equity loan remaining balance $37,600
We would like to refinance the primary mortgage and take out $275,000 but subordinate the home equity loan (I do not want to roll that loan into the refinance)
One lender has said this would be fine but closing costs were very high.
Another lender said the home equity loan would have to be rolled into a cash out refinance.
I have found sources online that discuss subordination in a situation like this, but am surprised and a bit worried that a lender would claim this is not possible.
The reason for the subordination is that the home equity line is part of a purchase assistance program from my employer and the payments are made by my employer, so rolling it into the new loan is not an option financially.
I just want to be clear on the rules surrounding this situation.