*This is grey area. If you need to build the emergency savings but don't have income to also fund the 401(k) beyond matching level, consider putting the savings into a Roth IRA, you may take out the initial deposit with no penalty. This would create the potential for longer term tax-free savings, while still having emergency money available.
"Accessible Funds" may mean savings or other sources of money to take you through an emergency. This can be an equity line, 401(k) loan, or other source of money.
Alternately, if you made deposits into the 401(k) with the same intent, you would be able to borrow, $10K or 50% of the account balance and pay it back usually at a favorable rate. The downside to this is if you lose your job, the loan is would be taken from the 401(k) account, taxed, and is subject to a 10% penalty. So, while I acknowledge it's an option, it's not recommended.
In the end, you want to be sure all your financial positions are in order before commiting money to the main mortgage. It's certainly a good feeling to 'burn' the mortgage lien, and it's a worthy goal, but it's not the 'no-brainer' it was when mortgage rates were 12% and higher. Do you homework, consider the alternatives, and decide wisely.