I honestly did a Mae Sae run last week and had nothing on me except 1000 baht for bus/food etc. Everything was fine... went out stayed for an hour in dusty Myanmar and turned back.
Just did Mae Sai border run last week. Easy no issues at all. Cross the border pay 500 baht to the burmese immigration (i had 1000 baht note and they gave me change). Stay in Myanmar for an hour or so and walk back in. Red buses take you to and from the bus station/border for 15 baht.